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

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

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integral of 7/((z-10)^7)

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

- \frac{7}{6 ( z - 10 ) ^{6}} + C

Solution steps

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

Take the constant out:

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

= 7 \cdot \int \frac{1}{( z - 10 ) ^{7}} d z

Apply u-substitution

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

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

Apply the Power Rule

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

= 7 (- \frac{1}{6 u ^{6}})

Substitute back

u = z - 10

= 7 (- \frac{1}{6 ( z - 10 ) ^{6}})

Simplify

7 (- \frac{1}{6 ( z - 10 ) ^{6}}) : - \frac{7}{6 ( z - 10 ) ^{6}}

= - \frac{7}{6 ( z - 10 ) ^{6}}

Add a constant to the solution

= - \frac{7}{6 ( z - 10 ) ^{6}} + C

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\frac{d}{d x} (x^{3} - 3 x^{2} - 9 x + 4)

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