What is the integral of (tan^3(θ))/(sec^4(θ)) ?

The integral of (tan^3(θ))/(sec^4(θ)) is (sin^4(θ))/4+C

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integral of (tan^3(θ))/(sec^4(θ))

\int \frac{tan ^{3} ( θ )}{sec ^{4} ( θ )} d θ

\frac{sin ^{4} ( θ )}{4} + C

Solution steps

\int \frac{tan ^{3} ( θ )}{sec ^{4} ( θ )} d θ

Rewrite using trig identities

= \int sin^{3} (θ) cos (θ) d θ

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 = sin (θ)

= \frac{sin ^{4} ( θ )}{4}

Add a constant to the solution

= \frac{sin ^{4} ( θ )}{4} + C

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What is the integral of (tan^3(θ))/(sec^4(θ)) ?
The integral of (tan^3(θ))/(sec^4(θ)) is (sin^4(θ))/4+C