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

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

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

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

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

Solution steps

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

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} (p)

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

Add a constant to the solution

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

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