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) \cdot (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

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

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