What is the integral of xsec^2(x^2+7) ?

The integral of xsec^2(x^2+7) is 1/2 tan(x^2+7)+C

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integral of xsec^2(x^2+7)

\int x sec^{2} (x^{2} + 7) d x

\frac{1}{2} tan (x^{2} + 7) + C

Solution steps

\int x sec^{2} (x^{2} + 7) d x

Apply u-substitution

= \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

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

Use the common integral:

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

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

Substitute back

u = x^{2} + 7

= \frac{1}{2} tan (x^{2} + 7)

Add a constant to the solution

= \frac{1}{2} tan (x^{2} + 7) + C

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What is the integral of xsec^2(x^2+7) ?
The integral of xsec^2(x^2+7) is 1/2 tan(x^2+7)+C