What is the integral of xsec^2(3x^2) ?

The integral of xsec^2(3x^2) is 1/6 tan(3x^2)+C

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integral of xsec^2(3x^2)

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

\frac{1}{6} tan (3 x^{2}) + C

Solution steps

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

Apply u-substitution

= \int \frac{sec ^{2} ( u )}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int sec^{2} (u) d u

Use the common integral:

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

= \frac{1}{6} tan (u)

Substitute back

u = 3 x^{2}

= \frac{1}{6} tan (3 x^{2})

Add a constant to the solution

= \frac{1}{6} tan (3 x^{2}) + C

What is the integral of xsec^2(3x^2) ?
The integral of xsec^2(3x^2) is 1/6 tan(3x^2)+C