What is the integral of tan(x)sec^5(x) ?

The integral of tan(x)sec^5(x) is (sec^5(x))/5+C

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integral of tan(x)sec^5(x)

\int tan (x) sec^{5} (x) d x

\frac{sec ^{5} ( x )}{5} + C

Solution steps

\int tan (x) sec^{5} (x) d x

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \frac{u ^{5}}{5}

Substitute back

u = sec (x)

= \frac{sec ^{5} ( x )}{5}

Add a constant to the solution

= \frac{sec ^{5} ( x )}{5} + C

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What is the integral of tan(x)sec^5(x) ?
The integral of tan(x)sec^5(x) is (sec^5(x))/5+C