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

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

Apply the Power Rule

: - \frac{1}{u}

= - \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

\frac{9 y ^{2} - t ^{2}}{y ^{5}} \frac{d y}{d t} + \frac{t}{2 y ^{4}} = 0

\frac{d y}{d x} - y = e^{x} \cdot y^{2}

\int_{4}^{\infty} 5 e^{- \frac{y}{2}} d y

\int \frac{x}{x + 2 y} d x

\frac{x ^{2} - 1}{x ^{3}}

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