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

The integral of 1/((2x+1)^3) is -1/(4(2x+1)^2)+C

integral of 1/((2x+1)^3)

integral

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

- \frac{1}{4 ( 2 x + 1 ) ^{2}} + C

Solution steps

\int \frac{1}{( 2 x + 1 ) ^{3}} d x

Apply u-substitution

= \int \frac{1}{2 u ^{3}} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u ^{3}} d u

Apply the Power Rule

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

Substitute back

u = 2 x + 1

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

Simplify

\frac{1}{2} (- \frac{1}{2 ( 2 x + 1 ) ^{2}}) : - \frac{1}{4 ( 2 x + 1 ) ^{2}}

= - \frac{1}{4 ( 2 x + 1 ) ^{2}}

Add a constant to the solution

= - \frac{1}{4 ( 2 x + 1 ) ^{2}} + C

in t e g r a l \frac{cos ( \frac{1}{x} )}{x ^{3}}

in t e g r a l \frac{1}{1 + cos ^{2} ( x )}

in t e g r a l x^{3} e^{x}

in t e g r a l \frac{1}{( x ^{2} + x + 2 )}

in t e g r a l \frac{ln ( x ^{2} )}{x ^{2}}

What is the integral of 1/((2x+1)^3) ?
The integral of 1/((2x+1)^3) is -1/(4(2x+1)^2)+C