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

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

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integral of tan(θ)sec^4(θ)

\int tan (θ) sec^{4} (θ) d θ

\frac{sec ^{4} ( θ )}{4} + C

Solution steps

\int tan (θ) sec^{4} (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 = sec (θ)

= \frac{sec ^{4} ( θ )}{4}

Add a constant to the solution

= \frac{sec ^{4} ( θ )}{4} + C

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