What is the integral of 1/((1+x)^3) ?

The integral of 1/((1+x)^3) is -1/(2(1+x)^2)+C

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integral of 1/((1+x)^3)

integral

\frac{1}{( 1 + x ) ^{3}}

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

Solution steps

\int \frac{1}{( 1 + x ) ^{3}} d x

Apply u-substitution

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

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

Apply the Power Rule

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

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

Substitute back

u = 1 + x

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

Add a constant to the solution

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

3 t + 4

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

2^{- x}

sin (y^{2})

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

What is the integral of 1/((1+x)^3) ?
The integral of 1/((1+x)^3) is -1/(2(1+x)^2)+C