What is the integral of (8000-2000x)/((x^2-8x+17)^2) ?

The integral of (8000-2000x)/((x^2-8x+17)^2) is (1000)/(x^2-8x+17)+C

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integral of (8000-2000x)/((x^2-8x+17)^2)

\int \frac{8000 - 2000 x}{( x ^{2} - 8 x + 17 ) ^{2}} d x

\frac{1000}{x ^{2} - 8 x + 17} + C

Solution steps

\int \frac{8000 - 2000 x}{( x ^{2} - 8 x + 17 ) ^{2}} d x

Apply u-substitution

: \int - \frac{1000}{u ^{2}} d u

= \int - \frac{1000}{u ^{2}} d u

Take the constant out:

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

= - 1000 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - 1000 (- \frac{1}{u})

Substitute back

u = x^{2} - 8 x + 17

= - 1000 (- \frac{1}{x ^{2} - 8 x + 17})

Simplify

- 1000 (- \frac{1}{x ^{2} - 8 x + 17}) : \frac{1000}{x ^{2} - 8 x + 17}

= \frac{1000}{x ^{2} - 8 x + 17}

Add a constant to the solution

= \frac{1000}{x ^{2} - 8 x + 17} + C

\frac{d}{d x} (x^{5} \cdot tan (x))

n = 1 \sum \infty 1

\int \frac{x ^{2}}{36 - 25 x ^{2}} d x

\int_{- 2}^{3} \frac{9}{x ^{4}} d x

4 cos (sin (2 x))

What is the integral of (8000-2000x)/((x^2-8x+17)^2) ?
The integral of (8000-2000x)/((x^2-8x+17)^2) is (1000)/(x^2-8x+17)+C