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

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

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

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

diverges

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int_{0}^{2} \frac{1}{u ^{2}} d u

= 4 \cdot \int_{0}^{2} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{0}^{2}

= 4 [- \frac{1}{u}]_{0}^{2}

Compute the boundaries:

diverges

= diverges

\int_{0}^{π} \frac{1}{x} d x

\int_{1}^{4} x^{3} ln (x) d x

\int_{0}^{1} x^{3} \cdot e^{- x} d x

\int_{1}^{3} x^{3} e^{- \frac{5}{3} x} d x

\int_{- 1}^{1} x e^{- inπ x} d x

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