What is the integral of (4+x^8)^58x^7 ?

The integral of (4+x^8)^58x^7 is 1/6 (4+x^8)^6+C

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integral of (4+x^8)^58x^7

\int (4 + x^{8})^{5} 8 x^{7} d x

\frac{1}{6} (4 + x^{8})^{6} + C

Solution steps

\int (4 + x^{8})^{5} \cdot 8 x^{7} d x

Take the constant out:

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

= 8 \cdot \int (4 + x^{8})^{5} x^{7} d x

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

: \frac{5}{6} u^{\frac{6}{5}}

= 8 \cdot \frac{1}{40} \cdot \frac{5}{6} u^{\frac{6}{5}}

Substitute back

u = (4 + x^{8})^{5}

= 8 \cdot \frac{1}{40} \cdot \frac{5}{6} ((4 + x^{8})^{5})^{\frac{6}{5}}

Simplify

8 \cdot \frac{1}{40} \cdot \frac{5}{6} ((4 + x^{8})^{5})^{\frac{6}{5}} : \frac{1}{6} (4 + x^{8})^{6}

= \frac{1}{6} (4 + x^{8})^{6}

Add a constant to the solution

= \frac{1}{6} (4 + x^{8})^{6} + C

\int (sec^{2} (θ) + 7) d θ

\int_{0}^{2} (3 x^{2} + 2 x) d x

\int - 3 cos^{2} (x) sin (x) d x

f (x) = 3 x^{3} + 6 x^{2} + 19

(x + y)^{2} d x + (2 x y + x^{2} - 2) d y = 0

What is the integral of (4+x^8)^58x^7 ?
The integral of (4+x^8)^58x^7 is 1/6 (4+x^8)^6+C