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

The integral of tan(θ)sec^3(θ) is 1/3 sec^3(θ)+C

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integral of tan(θ)sec^3(θ)

\int tan (θ) sec^{3} (θ) d θ

\frac{1}{3} sec^{3} (θ) + C

Solution steps

\int tan (θ) sec^{3} (θ) d θ

Apply u-substitution

= \int \frac{1}{3} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{3} u

Substitute back

u = sec^{3} (θ)

= \frac{1}{3} sec^{3} (θ)

Add a constant to the solution

= \frac{1}{3} sec^{3} (θ) + C

What is the integral of tan(θ)sec^3(θ) ?
The integral of tan(θ)sec^3(θ) is 1/3 sec^3(θ)+C