What is the integral of-20 1/((1+2x)^2) ?

The integral of-20 1/((1+2x)^2) is (10)/(1+2x)+C

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integral of-20 1/((1+2x)^2)

\int - 20 \frac{1}{( 1 + 2 x ) ^{2}} d x

\frac{10}{1 + 2 x} + C

Solution steps

\int - 20 \cdot \frac{1}{( 1 + 2 x ) ^{2}} d x

Take the constant out:

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

= - 20 \cdot \int \frac{1}{( 1 + 2 x ) ^{2}} d x

Apply u-substitution

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

= - 20 \cdot \int \frac{1}{2 u ^{2}} d u

Take the constant out:

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

= - 20 \cdot \frac{1}{2} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - 20 \cdot \frac{1}{2} (- \frac{1}{u})

Substitute back

u = 1 + 2 x

= - 20 \cdot \frac{1}{2} (- \frac{1}{1 + 2 x})

Simplify

- 20 \cdot \frac{1}{2} (- \frac{1}{1 + 2 x}) : \frac{10}{1 + 2 x}

= \frac{10}{1 + 2 x}

Add a constant to the solution

= \frac{10}{1 + 2 x} + C

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What is the integral of-20 1/((1+2x)^2) ?
The integral of-20 1/((1+2x)^2) is (10)/(1+2x)+C