If ∫ (d x/(x+2)(x2+1))=a log |1+x2|+b tan -1 x+(1/5) log |x+2|+c, then

Question

If ∫ (d x/(x+2)(x2+1))=a log |1+x2|+b tan -1 x+(1/5) log |x+2|+c, then (A) a =(-1/10) b =(2/5) (B) a=(-1/10) b=(-2/5) (C) a=(1/10) b=(2/5) (D) a=(1/10) b=(-2/5)

Tardigrade Admin · Accepted Answer

(1/(x+2)(x2+1))=(A/x+2)+(B x+C/x2+1) A=(1/5), B=(-1/5), C=(2/5)

Q. If $\int \frac{d x}{( x + 2 ) ( x ^{2} + 1 )} = a lo g ∣ ∣ 1 + x^{2} ∣ ∣ + b tan^{- 1} x + \frac{1}{5} lo g ∣ x + 2∣ + c$ , then

$a = \frac{- 1}{10} b = \frac{2}{5}$

$a = \frac{- 1}{10} b = \frac{- 2}{5}$

$a = \frac{1}{10} b = \frac{2}{5}$

$a = \frac{1}{10} b = \frac{- 2}{5}$

$\frac{1}{( x + 2 ) ( x ^{2} + 1 )} = \frac{A}{x + 2} + \frac{B x + C}{x ^{2} + 1}$
$A = \frac{1}{5}, B = \frac{- 1}{5}, C = \frac{2}{5}$

Q. If ∫(x+2)(x2+1)dx​=alog∣∣​1+x2∣∣​+btan−1x+51​log∣x+2∣+c, then

a=10−1​b=52​

a=10−1​b=5−2​

a=101​b=52​

a=101​b=5−2​