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

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

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

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

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

Solution steps

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

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

Add a constant to the solution

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

\int \frac{ln ( x ^{18} )}{x} d x

\int (2 x^{3} - 4 x + 3 x) d x

\frac{\partial}{\partial y} (\frac{x ^{2} y}{x ^{2} + y ^{2}})

\frac{d y}{d x} = \frac{e ^{- 2 x}}{1 + e ^{- 2 x}}

10 cos (x)

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