What is the integral of (x^2e^{x^3}+x^2sin(y)) ?

The integral of (x^2e^{x^3}+x^2sin(y)) is 1/3 x^3sin(y)+1/3 e^{x^3}+C

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integral of (x^2e^{x^3}+x^2sin(y))

\int (x^{2} e^{x^{3}} + x^{2} sin (y)) d x

\frac{1}{3} x^{3} sin (y) + \frac{1}{3} e^{x^{3}} + C

Solution steps

\int x^{2} e^{x^{3}} + x^{2} sin (y) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (y) x^{2} d x + \int e^{x^{3}} x^{2} d x

\int sin (y) x^{2} d x = \frac{1}{3} x^{3} sin (y)

\int e^{x^{3}} x^{2} d x = \frac{1}{3} e^{x^{3}}

= \frac{1}{3} x^{3} sin (y) + \frac{1}{3} e^{x^{3}}

Add a constant to the solution

= \frac{1}{3} x^{3} sin (y) + \frac{1}{3} e^{x^{3}} + C

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What is the integral of (x^2e^{x^3}+x^2sin(y)) ?
The integral of (x^2e^{x^3}+x^2sin(y)) is 1/3 x^3sin(y)+1/3 e^{x^3}+C