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

The integral of tan(x)+x^2 is -ln|cos(x)|+(x^3)/3+C

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integral of tan(x)+x^2

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

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

Solution steps

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

\int tan (x) d x = - ln ∣ cos (x) ∣

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

= - ln ∣ cos (x) ∣ + \frac{x ^{3}}{3}

Add a constant to the solution

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

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What is the integral of tan(x)+x^2 ?
The integral of tan(x)+x^2 is -ln|cos(x)|+(x^3)/3+C