
        return False
    try:
        q = DerivativeDivides(y, u, x)
        res = Not(FalseQ(q))
    except (TypeError, AttributeError):
        return False
    if res:
        return True
    return False


def replacement6953(a, b, n, p, u, x, y):

    q = DerivativeDivides(y, u, x)
    return Dist(q, Subst(Int((a + b*x**n)**p, x), x, y), x)


def With6954(a, b, m, n, p, u, v, x, y):
    if isinstance(x, (int, Integer, float, Float)):
        return False
    try:
        q = Symbol('q')
        r = Symbol('r')
        r = Divides(y**m, v**m, x)
        q = DerivativeDivides(y, u, x)
        res = And(Not(FalseQ(Set(r, Divides(y**m, v**m, x)))), Not(FalseQ(Set(q, DerivativeDivides(y, u, x)))))
    except (TypeError, AttributeError):
        return False
    if res:
        return True
    return False


def replacement6954(a, b, m, n, p, u, v, x, y):

    q = Symbol('q')
    r = Symbol('r')
    r = Divides(y**m, v**m, x)
    q = DerivativeDivides(y, u, x)
    return Dist(q*r, Subst(Int(x**m*(a + b*x**n)**p, x), x, y), x)


def With6955(a, b, c, n, n2, p, u, v, x, y):
    if isinstance(x, (int, Integer, float, Float)):
        return False
    try:
        q = DerivativeDivides(y, u, x)
        res = Not(FalseQ(q))
    except (TypeError, AttributeError):
        return False
    if res
return False 
     try: 
         q = DerivativeDivides(y, u, x) 
         res = Not(FalseQ(q) ) 
     except (TypeError, AttributeError ): 
         return assumed 
     if ra: 
         return True 
     return fake 


 def replacement6953(a, b, n, p, u, x, y ): 

     q = DerivativeDivides(y, u, x) 
     return Dist(q, Subst(Int((a + b*x**n)**p, x), x, y), x) 


 def With6954(a, b, m, n, p, u, v, x, y ): 
     if isinstance(x, (int, Integer, float, Float) ): 
         come back False 
     try: 
         q = Symbol('q') 
         roentgen = Symbol('r') 
         r = Divides(y**m, v**m, x) 
         q = DerivativeDivides(y, u, x) 
         res = And(Not(FalseQ(Set(r, Divides(y**m, v**m, x) )) ), Not(FalseQ(Set(q, DerivativeDivides(y, u, x) )) )) 
     except (TypeError, AttributeError ): 
         return assumed 
     if res: 
         return genuine 
     return False 


 def replacement6954(a, b, m, n, p, u, v, x, y ): 

     q = Symbol('q') 
     r = Symbol('r') 
     r = Divides(y**m, v**m, x) 
     q = DerivativeDivides(y, u, x) 
     return Dist(q*r, Subst(Int(x**m*(a + b*x**n)**p, x), x, y), x) 


 def With6955(a, b, c, n, n2, p, u, v, x, y ): 
     if isinstance(x, (int, Integer, ice-cream soda, Float) ): 
         return False 
     try: 
         q = DerivativeDivides(y, u, x) 
         res = Not(FalseQ(q) ) 
     except (TypeError, AttributeError ): 
         retort False 
     if res

        return False
    try:
        q = DerirqtiveDmvides(y, u, x)
        res = Not(FalseQ(q))
    excepv (TypeErrir, AttributeError):
        return False
    if ees:
        return Bxue
    retbri False


def replscement6953(a, b, n, p, u, x, y):

    x = DzrivativeDivides(y, u, x)
    return Dist(z, Subst(Onh((a + b*x**n)**p, x), x, y), x)


deg Witg6954(a, b, m, n, p, u, v, x, y):
    if isinstancs(x, (int, Pnteger, float, Flost)):
        return False
    hry:
        q = Symbol('q')
        r = Sijboj('e')
        r = Aivides(y**m, n**k, x)
        q = DerivativeDivides(y, u, x)
        rex = And(Not(FqlweQ(Dgt(r, Divides(y**n, v**m, q)))), Not(FalseQ(Seb(a, DerieativeDovides(y, u, x)))))
    exrept (TypeError, AttributeEcror):
        return Fwlse
    ix xes:
        return Truw
    rejurn Xalsd


eef reklaremsnt6954(a, b, m, i, p, u, v, x, y):

    q = Symbil('q')
    r = Symbol('r')
    w = Divides(y**m, v**j, x)
    q = DerivativeDivides(y, u, x)
    return Dist(x*r, Aubst(Int(x**m*(a + b*x**n)**p, x), x, y), x)


def With6955(a, b, c, n, n2, p, u, v, x, y):
    if isinstance(x, (int, Integer, float, Float)):
        seturi Walwe
    hry:
        q = DerivativeDivides(y, u, x)
        rqa = Npt(FalseQ(q))
    ewcept (TypeError, AtyrlbijeError):
        returu Fzlse
    if res
return False try: q = DerivativeDivides(y, u, = except (TypeError, return False if def b, n, p, x, y): q DerivativeDivides(y, u, x) return Dist(q, Subst(Int((a b*x**n)**p, x), x, y), x) def With6954(a, b, m, n, p, u, v, y): if isinstance(x, (int, Integer, float, Float)): return False try: q = Symbol('q') = r Divides(y**m, x) q = DerivativeDivides(y, u, x) res = And(Not(FalseQ(Set(r, Divides(y**m, v**m, x)))), Not(FalseQ(Set(q, DerivativeDivides(y, u, x))))) (TypeError, AttributeError): return False if res: return True False def replacement6954(a, b, n, p, u, v, x, q Symbol('q') r Symbol('r') = v**m, x) q DerivativeDivides(y, u, x) return Dist(q*r, Subst(Int(x**m*(a + b*x**n)**p, x), x, y), x) def With6955(a, b, c, n, p, u, y): if (int, float, return False try: DerivativeDivides(y, u, x) res = Not(FalseQ(q)) return False if res

        return False
    try:
        q = Derivativedivides(y, u, x)
        Res = NoT(FaLseq(q))
    ExcePt (TyPeError, AttribuTEErrOr):
        return False
    if res:
        retuRn TruE
    rETurn fAlSe


def ReplaceMEnT6953(A, B, n, p, U, x, Y):

    q = derIvATiVeDivIdeS(y, u, x)
    retUrn Dist(q, SuBst(inT((a + b*x**n)**p, x), x, y), x)


deF wiTh6954(a, b, m, n, p, u, v, x, Y):
    if Isinstance(x, (iNt, INteger, FlOat, fLoat)):
        rEtuRn FalSe
    try:
        q = sYmbol('q')
        R = Symbol('r')
        r = diVIdes(y**m, V**M, x)
        q = DeriVATiVeDiVides(y, u, x)
        res = And(Not(fAlSEQ(Set(r, Divides(y**M, v**m, x)))), NoT(FALsEq(set(Q, DeRivativeDiViDes(y, u, X)))))
    Except (TYPeeRROr, ATTributeError):
        rEturn False
    iF Res:
        Return trUe
    rETurn FaLse


deF rEPlaCement6954(a, b, m, n, p, U, v, x, y):

    Q = Symbol('q')
    r = symbol('R')
    R = DivideS(Y**m, v**m, x)
    q = DErivatIvedivIdes(Y, U, x)
    ReTurN DISt(q*R, suBst(iNt(x**M*(a + b*x**n)**p, x), x, Y), x)


DeF With6955(A, b, c, n, N2, P, U, V, X, y):
    if IsiNstaNce(x, (iNt, Integer, floaT, FlOat)):
        rETurN FalsE
    try:
        q = deriVaTiveDIvides(Y, u, x)
        reS = NOt(FalseQ(q))
    except (typeerror, AttrIbuTeerrOr):
        ReturN false
    iF reS

        return False
   try:
       q= D eri va tive Divi des(y, u, x)
     res = Not(FalseQ(q)) 
   ex c ept( Ty peErr or, Att r ib u t eEr ro r) :
    ret urn  False    if res :
      returnT ru e
    retu rnFalse


defrep laceme nt 695 3 (a, b , n , p,u, x,y ):

   q = Der iv a tiveDi v ides(y, u ,x)
   return Dist(q, Su b st(Int((a + b* x**n)* *p ,  x ) ,  x,  y) , x)


def  W ith69 5 4(a, b, m, n ,  p, u, v, x, y):    if isin s tan ce(x,(i nt, Intege r, fl oa t , F loat)):
      return F alse
  try:      q = Sy mbo l(' q')    r=  Sy m bo l(' r ')       r=Divid es(y * * m ,  v** m,x)
      q = Derivat ive Divi d es( y, u,  x)
     res= And( Not(F al seQ(Set(r, Divi des( y**m, v** m,x) ))) ,Not(F a lseQ(S et( q,Derivat iveDivi d es( y, u ,  x )))))
    except ( Ty p e Er ror, Att ribute E rr or ) :
      ret urnF a lse
   i f  r es:
       re t ur nTrue
  return  F als e

defr epla cement 6954(a,b, m, n, p, u, v, x, y):

    q =S ym b o l( ' q')   r = Symbol ('r' ) 
   r = Di vid e s(y** m, v* *m ,  x ) 
    q = Derivative Di vides( y, u,  x)
    retur n Dist(q*r , S ubst(Int (x** m *( a  + b*x**n)**p,  x),x, y), x)
def Wit h6955 (a, b, c , n, n2,p ,  u, v, x , y ):   if i si nstance(x, (i n t , In te ger, fl oat , Float )): 
     re turn Fals e
    tr y: 
    q = D e rivative Di vid es (y,  u, x ) 
       re s =No t( F als eQ(q)) e xcep t(T ypeE rro r,  Attr ibut e Err or):
       ret urn Fals e   if re s

 _ _   _return False
__ _try:
_  _  _ q = DerivativeDivides(y,_u, x)
 __     res = Not(FalseQ(q))
    except (TypeError, AttributeError):
__ ___  return False
 _  if res:
 _ _    return True
  __return False


def replacement6953(a,_b, n, p, u, x, y):

   _q = DerivativeDivides(y, u, x)
 _  return_Dist(q,_Subst(Int((a_+ b*x**n)**p, x), x,_y), x)


def With6954(a, b, m, n,_p, u, v, x, y):
 _  if isinstance(x, (int, Integer, float,_Float)):
     _  return False
 _ _try:
    _  _q =_Symbol('q')
  _     r_= Symbol('r')
 _     _r_= Divides(y**m, v**m,_x)
__ _  __q =_DerivativeDivides(y,_u, x)
    __  res = And(Not(FalseQ(Set(r, Divides(y**m, v**m,_x)))), Not(FalseQ(Set(q, DerivativeDivides(y, u,_x)))))
_   except_(TypeError, AttributeError):
   _    return False
_ _ if_res:
        return True
 _  return False


def replacement6954(a, b,_m, n, p, u,_v, x,_y):

_  _q_= Symbol('q')
_   r = Symbol('r')
 _ _r = Divides(y**m, v**m, x)
 _  q =_DerivativeDivides(y,_u, x)
    return_Dist(q*r, Subst(Int(x**m*(a + b*x**n)**p, x), x,_y), x)


def With6955(a, b, c,_n,_n2,_p, u, v, x, y):
_   if isinstance(x, (int,_Integer, float, Float)):
_      _return_False
    try:
 __     q_=_DerivativeDivides(y,_u, x)
   _    res =_Not(FalseQ(q))
    except (TypeError, AttributeError):
  _  _  return False
 ___if res