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

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

Popular >

integral of (4x+3)/((x-2)^3)

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

- \frac{4 x + 3}{2 ( x - 2 ) ^{2}} - \frac{2}{x - 2} + C

Solution steps

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

Apply Integration By Parts

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

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

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

= - \frac{4 x + 3}{2 ( x - 2 ) ^{2}} - \frac{2}{x - 2}

Add a constant to the solution

= - \frac{4 x + 3}{2 ( x - 2 ) ^{2}} - \frac{2}{x - 2} + C

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

\int 5 x e^{0.005 x^{2}} d x

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

\int \frac{e ^{b t}}{( a - e ^{b t} ) ^{5}} d t

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