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

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

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

integral

tan (x) sec^{2} (x)

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

Solution steps

\int tan (x) sec^{2} (x) 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^2(x) ?
The integral of tan(x)sec^2(x) is (tan^2(x))/2+C