What is the integral from 0 to 3 of pi(1/(x+5))^2 ?

The integral from 0 to 3 of pi(1/(x+5))^2 is (3pi)/(40)

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integral from 0 to 3 of pi(1/(x+5))^2

\int_{0}^{3} π (\frac{1}{x + 5})^{2} d x

\frac{3 π}{40}

Decimal Notation

0.23561 \dots

Solution steps

\int_{0}^{3} π (\frac{1}{x + 5})^{2} d x

Take the constant out:

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

= π \cdot \int_{0}^{3} (\frac{1}{x + 5})^{2} d x

Simplify

(\frac{1}{x + 5})^{2} : \frac{1}{( x + 5 ) ^{2}}

= π \cdot \int_{0}^{3} \frac{1}{( x + 5 ) ^{2}} d x

Apply u-substitution

: \int_{5}^{8} \frac{1}{u ^{2}} d u

= π \cdot \int_{5}^{8} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{5}^{8}

= π [- \frac{1}{u}]_{5}^{8}

Compute the boundaries:

\frac{3}{40}

= π \frac{3}{40}

Simplify

= \frac{3 π}{40}

y = 3 x + 1, y = x + 1

\int 5 u^{5} u^{6} + 5 d u

\frac{d}{d x} (\frac{π}{( 2 x ) ^{4}})

\frac{d y}{d x} = 2 x y - 6 x

\frac{1}{( 1 - x ) ^{4}}

What is the integral from 0 to 3 of pi(1/(x+5))^2 ?
The integral from 0 to 3 of pi(1/(x+5))^2 is (3pi)/(40)