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

The integral of tan(x)(sec(x))^2 is (tan^2(x))/2+C

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integral of tan(x)(sec(x))^2

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

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

Solution steps

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

Apply u-substitution

= \int u d u

Apply the Power Rule

= \frac{u ^{2}}{2}

Substitute back

u = tan (x)

= \frac{tan ^{2} ( x )}{2}

Add a constant to the solution

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

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\frac{d}{d x} (x^{n})

\int_{0}^{2} x^{5} \cdot e^{x^{2}} d x

What is the integral of tan(x)(sec(x))^2 ?
The integral of tan(x)(sec(x))^2 is (tan^2(x))/2+C