Question

Solve the Integral:


(2x/x^2 + 3x + 2)


Chapter => Integrals.

Answer 1

HELLO DEAR,

GIVEN:- integral is {2x/(x² + 3x + 2)}.dx

$\bold{\int \{2x/(x^2 + 2x + x + 2)\}.dx}$

$\bold{\int \{2x/(x + 2)(x + 1)\}.dx}$

solving by partial fraction;

2x/(x + 2)(x + 1) = A/(x + 2) + B/(x + 1)

2x = A(x + 1) + B(x + 2)

2x = x(A + B) + (A + 2B)

on comparing both side like Power of cofficient of x,

A + B = 2-----(1) , A + 2B = 0------(2)

on solving we get,

B = -2 , A = 4

now, $\bold{\int \{4/(x + 2) - 2/(x + 1)\}.dx}$

$\bold{\{4log|x + 2| - 2log|x + 1| + c.\}}$

where, C is arbitrary constant.

I HOPE IT'S HELP YOU DEAR,

THANK

Answer 2

hello friend from attachment