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

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

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integral of x^2+tan(2x)

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

\frac{x ^{3}}{3} - \frac{1}{2} ln ∣ cos (2 x) ∣ + C

Solution steps

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

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

\int tan (2 x) d x = - \frac{1}{2} ln ∣ cos (2 x) ∣

= \frac{x ^{3}}{3} - \frac{1}{2} ln ∣ cos (2 x) ∣

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{1}{2} ln ∣ cos (2 x) ∣ + C

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