What is the integral of (24)/((x+2)^5) ?

The integral of (24)/((x+2)^5) is 24(x/((x+2)^5)-5/(4(x+2)^4)+2/((x+2)^5))+C

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integral of (24)/((x+2)^5)

\int \frac{24}{( x + 2 ) ^{5}} d x

24 (\frac{x}{( x + 2 ) ^{5}} - \frac{5}{4 ( x + 2 ) ^{4}} + \frac{2}{( x + 2 ) ^{5}}) + C

Solution steps

\int \frac{24}{( x + 2 ) ^{5}} d x

Take the constant out:

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

= 24 \cdot \int \frac{1}{( x + 2 ) ^{5}} d x

Apply Integration By Parts

: \frac{x}{( x + 2 ) ^{5}} - \int - \frac{5 x}{( x + 2 ) ^{6}} d x

= 24 (\frac{x}{( x + 2 ) ^{5}} - \int - \frac{5 x}{( x + 2 ) ^{6}} d x)

\int - \frac{5 x}{( x + 2 ) ^{6}} d x = \frac{5}{4 ( x + 2 ) ^{4}} - \frac{2}{( x + 2 ) ^{5}}

= 24 (\frac{x}{( x + 2 ) ^{5}} - (\frac{5}{4 ( x + 2 ) ^{4}} - \frac{2}{( x + 2 ) ^{5}}))

Simplify

= 24 (\frac{x}{( x + 2 ) ^{5}} - \frac{5}{4 ( x + 2 ) ^{4}} + \frac{2}{( x + 2 ) ^{5}})

Add a constant to the solution

= 24 (\frac{x}{( x + 2 ) ^{5}} - \frac{5}{4 ( x + 2 ) ^{4}} + \frac{2}{( x + 2 ) ^{5}}) + C

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What is the integral of (24)/((x+2)^5) ?
The integral of (24)/((x+2)^5) is 24(x/((x+2)^5)-5/(4(x+2)^4)+2/((x+2)^5))+C