Question

$\int_{}^{}\frac{dx}{(x + 1)(x–2)}$= A log (x + 1) + Blog(x–2) +c then -

• A. A + B = 0 ; A : B = – 1
• B. A B = 1 ; A : B = – 1
• C. A – B = 0 ; A : B = – 1
• D. None of these

Answer 1

Answer: (A)

A + B = 0 ; A : B = – 1

Answer 2

I = $\frac { 1 } { 3 }$ $\int \frac { ( x + 1 ) - ( x - 2 ) } { ( x + 1 ) ( x - 2 ) }$ dx

= $\frac { 1 } { 3 }$ $\int \left( \frac { 1 } { ( x - 2 ) } - \frac { 1 } { x + 1 } \right)$ dx

= $\frac { 1 } { 3 }$ log(x – 2) – $\frac { 1 } { 3 }$ log(x + 1) + c

Ž B = $\frac { 1 } { 3 }$ & A = – 1/3