ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Integrals of Polynomial Functions Calculator

## Get detailed solutions to your math problems with our Integrals of Polynomial Functions step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

Go!
Symbolic mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Difficult Problems

1

Here, we show you a step-by-step solved example of integrals of polynomial functions. This solution was automatically generated by our smart calculator:

$\int\left(x^2+2x+1\right)dx$
2

Expand the integral $\int\left(x^2+2x+1\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately

$\int x^2dx+\int2xdx+\int1dx$

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $2$

$\frac{x^{3}}{3}$
3

The integral $\int x^2dx$ results in: $\frac{x^{3}}{3}$

$\frac{x^{3}}{3}$

The integral of a function times a constant ($2$) is equal to the constant times the integral of the function

$2\int xdx$

Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, in this case $n=1$

$2\cdot \left(\frac{1}{2}\right)x^2$

Multiply the fraction and term in $2\cdot \left(\frac{1}{2}\right)x^2$

$x^2$
4

The integral $\int2xdx$ results in: $x^2$

$x^2$

The integral of a constant is equal to the constant times the integral's variable

$x$
5

The integral $\int1dx$ results in: $x$

$x$
6

Gather the results of all integrals

$\frac{x^{3}}{3}+x^2+x$
7

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\frac{x^{3}}{3}+x^2+x+C_0$

##  Final answer to the problem

$\frac{x^{3}}{3}+x^2+x+C_0$

### Are you struggling with math?

Access detailed step by step solutions to thousands of problems, growing every day!
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}