Integrate the rational function: frac{x}{(x+1 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $\frac{x}{(x+1)(x+2)} = \frac{A}{x+1} + \frac{B}{x+2}$.Multiplying both sides by $(x+1)(x+2)$,we get $x = A(x+2) + B(x+1)$.To find $A$,put $x

Vedclass · Accepted Answer

$\log \frac{(x+2)^2}{|x+1|} + C$

Vedclass · Answer

(C) Let $\frac{x}{(x+1)(x+2)} = \frac{A}{x+1} + \frac{B}{x+2}$.Multiplying both sides by $(x+1)(x+2)$,we get $x = A(x+2) + B(x+1)$.To find $A$,put $x = -1$: $-1 = A(-1+2) \Rightarrow A = -1$.To find $B$,put $x = -2$: $-2 = B(-2+1) \Rightarrow -2 = -B \Rightarrow B = 2$.Thus,$\frac{x}{(x+1)(x+2)} = \frac{-1}{x+1} + \frac{2}{x+2}$.Integrating both sides with respect to $x$:$\int \frac{x}{(x+1)(x+2)} dx = \int \left( \frac{-1}{x+1} + \frac{2}{x+2} \right) dx$.$= -\log |x+1| + 2\log |x+2| + C$.$= \log |x+2|^2 - \log |x+1| + C$.$= \log \left| \frac{(x+2)^2}{x+1} \right| + C$.

Integrate the rational function: $\frac{x}{(x+1)(x+2)}$

Similar Questions

$\int \frac{x + 2}{x^2 - 7x + 12} dx$ is equal to

$ \int \frac{x^2+1}{x(x^2-1)} dx $

$\int_{\log 4}^{\log 5} \frac{e^{2 x}+e^x}{e^{2 x}-5 e^x+6} d x=$

If $\int {\frac{{2x + 3}}{{(x - 1)({x^2} + 1)}}dx = {{\log }_e}\left\{ {{{(x - 1)}^{\frac{5}{2}}}{{({x^2} + 1)}^a}} \right\}} - \frac{1}{2}{\tan ^{ - 1}}x + A$,where $A$ is any arbitrary constant,then the value of $a$ is

$\int \frac{x-1}{(x-2)(x-3)} \, dx$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module