What is the integral of (sin(x^3)x^2+ln(x)) ?

The integral of (sin(x^3)x^2+ln(x)) is -1/3 cos(x^3)+xln(x)-x+C

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integral of (sin(x^3)x^2+ln(x))

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

- \frac{1}{3} cos (x^{3}) + x ln (x) - x + C

Solution steps

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

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

\int ln (x) d x = x ln (x) - x

= - \frac{1}{3} cos (x^{3}) + x ln (x) - x

Add a constant to the solution

= - \frac{1}{3} cos (x^{3}) + x ln (x) - x + C

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What is the integral of (sin(x^3)x^2+ln(x)) ?
The integral of (sin(x^3)x^2+ln(x)) is -1/3 cos(x^3)+xln(x)-x+C