What is the integral of sin(x)(sec(x))^3 ?

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

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integral of sin(x)(sec(x))^3

\int sin (x) (sec (x))^{3} d x

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

Solution steps

\int sin (x) (sec (x))^{3} d x

Rewrite using trig identities

= \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 sin(x)(sec(x))^3 ?
The integral of sin(x)(sec(x))^3 is (tan^2(x))/2+C