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Popular >

integral of (2+2x)/(-x^2-2x+1)

Solution

\int \frac{2 + 2 x}{- x ^{2} - 2 x + 1} d x

Solution

- ln - x^{2} - 2 x + 1 + C

Solution steps

\int \frac{2 + 2 x}{- x ^{2} - 2 x + 1} d x

Apply u-substitution

: \int - \frac{1}{u} d u

= \int - \frac{1}{u} d u

Take the constant out:

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

= - \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = - x^{2} - 2 x + 1

= - ln - x^{2} - 2 x + 1

Add a constant to the solution

= - ln - x^{2} - 2 x + 1 + C

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Frequently Asked Questions (FAQ)

What is the integral of (2+2x)/(-x^2-2x+1) ?
The integral of (2+2x)/(-x^2-2x+1) is -ln|-x^2-2x+1|+C