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

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

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

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

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

Solution steps

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

Integral of a constant:

\int a d x = a x

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

Simplify

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

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

Add a constant to the solution

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

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