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# Integrate : $\int e^{2x} \cos 5x dx$

$(a)\;\frac{e^{2x}}{2g}(2 \sin 5x + 5 \sin 5 x )+c \\(b)\;\frac{e^{2x}}{2g}(2 \cos 5x + 5 \sin 5 x )+c \\(c)\;\frac{e^{2x}}{2g}(2 \sin 5x + 5 \cos 5 x )+c \\ (d)\;None$

$\int \large\frac{x^3 \sin ^{-1}(x^2)}{\sqrt {1-x^4}}$$dx By using formula :- \int e^{ax} \cos bx dx = \large\frac{e^{ax}}{a^2+b^2}$$(a \cos b x+ b \sin bx)$$+c Put a=2; b=5 \large\frac{e^{2x}}{2g}$$(2 \cos 5x + 5 \sin 5 x )+c$
Hence b is the correct answer.
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