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

The integral of tan(x)sec(x)sec^2(x) is (sec^3(x))/3+C

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

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

\frac{sec ^{3} ( x )}{3} + C

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = sec (x)

= \frac{sec ^{3} ( x )}{3}

Add a constant to the solution

= \frac{sec ^{3} ( x )}{3} + C

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What is the integral of tan(x)sec(x)sec^2(x) ?
The integral of tan(x)sec(x)sec^2(x) is (sec^3(x))/3+C