What is the integral from 0 to 4 of 2/((x+2)^2) ?

The integral from 0 to 4 of 2/((x+2)^2) is 2/3

Popular >

integral from 0 to 4 of 2/((x+2)^2)

\int_{0}^{4} \frac{2}{( x + 2 ) ^{2}} d x

\frac{2}{3}

Decimal Notation

0.66666 \dots

Solution steps

\int_{0}^{4} \frac{2}{( x + 2 ) ^{2}} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{4} \frac{1}{( x + 2 ) ^{2}} d x

Apply u-substitution

: \int_{2}^{6} \frac{1}{u ^{2}} d u

= 2 \cdot \int_{2}^{6} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{2}^{6}

= 2 [- \frac{1}{u}]_{2}^{6}

Compute the boundaries:

\frac{1}{3}

= 2 \cdot \frac{1}{3}

Simplify

= \frac{2}{3}

\int_{0}^{2} 3 x (x^{2} + 1)^{3} d x

\int_{1}^{2} (4 - x^{2}) d x

\int_{- 1}^{2} x - 4 ∣ x ∣ d x

\int_{\frac{1}{x}}^{x^{2}} sin (t) d t

\int_{2}^{4} 4^{4 x} d x

What is the integral from 0 to 4 of 2/((x+2)^2) ?
The integral from 0 to 4 of 2/((x+2)^2) is 2/3