What is the integral of (xsin(x^2)+tan^2(x)) ?

The integral of (xsin(x^2)+tan^2(x)) is -1/2 cos(x^2)-x+tan(x)+C

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integral of (xsin(x^2)+tan^2(x))

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

- \frac{1}{2} cos (x^{2}) - x + tan (x) + C

Solution steps

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

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

\int tan^{2} (x) d x = - x + tan (x)

= - \frac{1}{2} cos (x^{2}) - x + tan (x)

Add a constant to the solution

= - \frac{1}{2} cos (x^{2}) - x + tan (x) + C

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What is the integral of (xsin(x^2)+tan^2(x)) ?
The integral of (xsin(x^2)+tan^2(x)) is -1/2 cos(x^2)-x+tan(x)+C