What is the integral of x^7sec^2(x^8) ?

The integral of x^7sec^2(x^8) is 1/8 tan(x^8)+C

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integral of x^7sec^2(x^8)

\int x^{7} sec^{2} (x^{8}) d x

\frac{1}{8} tan (x^{8}) + C

Solution steps

\int x^{7} sec^{2} (x^{8}) d x

Apply u-substitution

: \int \frac{sec ^{2} ( u )}{8} d u

= \int \frac{sec ^{2} ( u )}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int sec^{2} (u) d u

Use the common integral:

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

= \frac{1}{8} tan (u)

Substitute back

u = x^{8}

= \frac{1}{8} tan (x^{8})

Add a constant to the solution

= \frac{1}{8} tan (x^{8}) + C

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What is the integral of x^7sec^2(x^8) ?
The integral of x^7sec^2(x^8) is 1/8 tan(x^8)+C