What is the integral of ((x-1))/((x^2-2x-35)^7) ?

The integral of ((x-1))/((x^2-2x-35)^7) is -1/(12(x^2-2x-35)^6)+C

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integral of ((x-1))/((x^2-2x-35)^7)

\int \frac{( x - 1 )}{( x ^{2} - 2 x - 35 ) ^{7}} d x

- \frac{1}{12 ( x ^{2} - 2 x - 35 ) ^{6}} + C

Solution steps

\int \frac{x - 1}{( x ^{2} - 2 x - 35 ) ^{7}} d x

Apply u-substitution

= \int \frac{u}{( u ^{2} - 36 ) ^{7}} d u

Apply u-substitution

= \int \frac{1}{2 ( v - 36 ) ^{7}} d v

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{( v - 36 ) ^{7}} d v

Apply u-substitution

= \frac{1}{2} \cdot \int \frac{1}{w ^{7}} d w

Apply the Power Rule

= \frac{1}{2} (- \frac{1}{6 w ^{6}})

Substitute back

= \frac{1}{2} - \frac{1}{6 ( ( x - 1 ) ^{2} - 36 ) ^{6}}

Simplify

\frac{1}{2} - \frac{1}{6 ( ( x - 1 ) ^{2} - 36 ) ^{6}} : - \frac{1}{12 ( x ^{2} - 2 x - 35 ) ^{6}}

= - \frac{1}{12 ( x ^{2} - 2 x - 35 ) ^{6}}

Add a constant to the solution

= - \frac{1}{12 ( x ^{2} - 2 x - 35 ) ^{6}} + C

What is the integral of ((x-1))/((x^2-2x-35)^7) ?
The integral of ((x-1))/((x^2-2x-35)^7) is -1/(12(x^2-2x-35)^6)+C