What is the integral of r^2sec^2(r^3) ?

The integral of r^2sec^2(r^3) is 1/3 tan(r^3)+C

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integral of r^2sec^2(r^3)

\int r^{2} sec^{2} (r^{3}) d r

\frac{1}{3} tan (r^{3}) + C

Solution steps

\int r^{2} sec^{2} (r^{3}) d r

Apply u-substitution

= \int \frac{sec ^{2} ( u )}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= \frac{1}{3} tan (u)

Substitute back

u = r^{3}

= \frac{1}{3} tan (r^{3})

Add a constant to the solution

= \frac{1}{3} tan (r^{3}) + C

What is the integral of r^2sec^2(r^3) ?
The integral of r^2sec^2(r^3) is 1/3 tan(r^3)+C