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

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

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

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

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

Solution steps

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

Rewrite using trig identities

= \int tan (x) sec^{4} (x) d x

Apply u-substitution

= \int u^{3} d u

Apply the Power Rule

= \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

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