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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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