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

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

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integral of 3xsec^2(x^2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= 3 \cdot \frac{1}{2} tan (u)

Substitute back

u = x^{2}

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

Simplify

3 \cdot \frac{1}{2} tan (x^{2}) : \frac{3}{2} tan (x^{2})

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

Add a constant to the solution

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

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