What is the integral of s(5s^2-8)^6 ?

The integral of s(5s^2-8)^6 is 1/70 (5s^2-8)^7+C

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integral of s(5s^2-8)^6

\int s (5 s^{2} - 8)^{6} d s

\frac{1}{70} (5 s^{2} - 8)^{7} + C

Solution steps

\int s (5 s^{2} - 8)^{6} d s

Apply u-substitution

: \int \frac{u ^{6}}{10} d u

= \int \frac{u ^{6}}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= \frac{1}{10} \cdot \frac{u ^{7}}{7}

Substitute back

u = 5 s^{2} - 8

= \frac{1}{10} \cdot \frac{( 5 s ^{2} - 8 ) ^{7}}{7}

Simplify

\frac{1}{10} \cdot \frac{( 5 s ^{2} - 8 ) ^{7}}{7} : \frac{1}{70} (5 s^{2} - 8)^{7}

= \frac{1}{70} (5 s^{2} - 8)^{7}

Add a constant to the solution

= \frac{1}{70} (5 s^{2} - 8)^{7} + C

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What is the integral of s(5s^2-8)^6 ?
The integral of s(5s^2-8)^6 is 1/70 (5s^2-8)^7+C