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

The integral of (sec^5(x))/(csc(x)) is (sec^4(x))/4+C

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integral of (sec^5(x))/(csc(x))

\int \frac{sec ^{5} ( x )}{csc ( x )} d x

\frac{sec ^{4} ( x )}{4} + C

Solution steps

\int \frac{sec ^{5} ( x )}{csc ( x )} d x

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = sec (x)

= \frac{sec ^{4} ( x )}{4}

Add a constant to the solution

= \frac{sec ^{4} ( x )}{4} + C

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What is the integral of (sec^5(x))/(csc(x)) ?
The integral of (sec^5(x))/(csc(x)) is (sec^4(x))/4+C