What is the integral of 1/((y-10)^7) ?

The integral of 1/((y-10)^7) is -1/(6(y-10)^6)+C

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integral of 1/((y-10)^7)

\int \frac{1}{( y - 10 ) ^{7}} d y

- \frac{1}{6 ( y - 10 ) ^{6}} + C

Solution steps

\int \frac{1}{( y - 10 ) ^{7}} d y

Apply u-substitution

: \int \frac{1}{u ^{7}} d u

= \int \frac{1}{u ^{7}} d u

Apply the Power Rule

: - \frac{1}{6 u ^{6}}

= - \frac{1}{6 u ^{6}}

Substitute back

u = y - 10

= - \frac{1}{6 ( y - 10 ) ^{6}}

Add a constant to the solution

= - \frac{1}{6 ( y - 10 ) ^{6}} + C

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What is the integral of 1/((y-10)^7) ?
The integral of 1/((y-10)^7) is -1/(6(y-10)^6)+C