What is the integral of (20000)/((x+100)^3) ?

The integral of (20000)/((x+100)^3) is -(10000)/((x+100)^2)+C

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integral of (20000)/((x+100)^3)

integral

\frac{20000}{( x + 100 ) ^{3}}

- \frac{10000}{( x + 100 ) ^{2}} + C

Solution steps

\int \frac{20000}{( x + 100 ) ^{3}} d x

Take the constant out:

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

= 20000 \cdot \int \frac{1}{( x + 100 ) ^{3}} d x

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= 20000 \cdot \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= 20000 (- \frac{1}{2 u ^{2}})

Substitute back

u = x + 100

= 20000 (- \frac{1}{2 ( x + 100 ) ^{2}})

Simplify

20000 (- \frac{1}{2 ( x + 100 ) ^{2}}) : - \frac{10000}{( x + 100 ) ^{2}}

= - \frac{10000}{( x + 100 ) ^{2}}

Add a constant to the solution

= - \frac{10000}{( x + 100 ) ^{2}} + C

\frac{( x ^{3} - x - 2 )}{( 1 - x ^{2} )}

x^{3} - 3 x^{2} + 5 x + 2

(e^{- t}) \cdot (\frac{1}{t})

x^{2} + a^{2}

(\frac{1}{x - 1})^{\frac{1}{2}}

What is the integral of (20000)/((x+100)^3) ?
The integral of (20000)/((x+100)^3) is -(10000)/((x+100)^2)+C