What is the integral of (2s-8)/((s^2-8s+25)^2) ?

The integral of (2s-8)/((s^2-8s+25)^2) is -1/(s^2-8s+25)+C

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integral of (2s-8)/((s^2-8s+25)^2)

\int \frac{2 s - 8}{( s ^{2} - 8 s + 25 ) ^{2}} d s

- \frac{1}{s ^{2} - 8 s + 25} + C

Solution steps

\int \frac{2 s - 8}{( s ^{2} - 8 s + 25 ) ^{2}} d s

Apply u-substitution

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

= - \frac{1}{u}

Substitute back

u = s^{2} - 8 s + 25

= - \frac{1}{s ^{2} - 8 s + 25}

Add a constant to the solution

= - \frac{1}{s ^{2} - 8 s + 25} + C

What is the integral of (2s-8)/((s^2-8s+25)^2) ?
The integral of (2s-8)/((s^2-8s+25)^2) is -1/(s^2-8s+25)+C