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

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

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

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

\frac{1}{3} sec^{3} (x) + C

Solution steps

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

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} (x)

= \frac{1}{3} sec^{3} (x)

Add a constant to the solution

= \frac{1}{3} sec^{3} (x) + C

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