What is the integral of (x^6)/(sqrt(6-x^7)) ?

The integral of (x^6)/(sqrt(6-x^7)) is -2/7 sqrt(6-x^7)+C

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integral of (x^6)/(sqrt(6-x^7))

\int \frac{x ^{6}}{6 - x ^{7}} d x

- \frac{2}{7} 6 - x^{7} + C

Solution steps

\int \frac{x ^{6}}{6 - x ^{7}} d x

Apply u-substitution

: \int - \frac{2}{7} d u

= \int - \frac{2}{7} d u

Integral of a constant:

\int a d x = a x

= (- \frac{2}{7}) u

Substitute back

u = 6 - x^{7}

= (- \frac{2}{7}) 6 - x^{7}

Simplify

= - \frac{2}{7} 6 - x^{7}

Add a constant to the solution

= - \frac{2}{7} 6 - x^{7} + C

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sin (3 x)

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What is the integral of (x^6)/(sqrt(6-x^7)) ?
The integral of (x^6)/(sqrt(6-x^7)) is -2/7 sqrt(6-x^7)+C