The correct option is C log |(x 2)^2x 1 |+C Let x/(x 1)(x 2)=A/(x 1)+B/(x 2) ⇒ x=A(x 2)+B(x 1) ............ (1)Substituting x=1 and 2 in ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Definite Integral as Limit of Sum

∫xdx/x-1x-2 e...

Question

$\int \frac{x d x}{(x - 1) (x - 2)}$ equals

log ∣ ∣ ∣ \frac{(x - 1)^{2}}{x - 2} ∣ ∣ ∣ + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

log ∣ ∣ ∣ \frac{(x - 2)^{2}}{x - 1} ∣ ∣ ∣ + C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

log ∣ ∣ ∣ {(\frac{x - 1}{x - 2})}^{2} ∣ ∣ ∣ + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

log | (x - 1) (x - 2) | + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $log ∣ ∣ ∣ \frac{(x - 2)^{2}}{x - 1} ∣ ∣ ∣ + C$
Let $\frac{x}{(x - 1) (x - 2)} = \frac{A}{(x - 1)} + \frac{B}{(x - 2)}$
$\Rightarrow x = A (x - 2) + B (x - 1)$ ............ (1)
Substituting $x = 1$ and 2 in (1), we obtain
$A = - 1$ and $B = 2$
$∴ \frac{x}{(x - 1) (x - 2)} = - \frac{1}{(x - 1)} + \frac{2}{(x - 2)}$
$\Rightarrow \int \frac{x}{(x - 1) (x - 2)} d x = \int {\frac{- 1}{(x - 1)} + \frac{2}{(x - 2)}} d x$
$= - log | x - 1 | + 2 log | x - 2 | + C$
$= log ∣ ∣ ∣ \frac{(x - 2)^{2}}{x - 1} ∣ ∣ ∣ + C$

Suggest Corrections

Similar questions

\int \frac{x^{3}}{x + 1} d x

(a) x + \frac{x^{2}}{2} + \frac{x^{3}}{3} - \log |1 - x| + C (b) x + \frac{x^{2}}{2} - \frac{x^{3}}{3} - \log |1 - x| + C (c) x - \frac{x^{2}}{2} - \frac{x^{3}}{3} - \log |1 + x| + C (d) x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - \log |1 + x| + C

\int_{0}^{3} \frac{3 x + 1}{x^{2} + 9} d x =

\frac{π}{12} + \log (2 \sqrt{2})

\frac{π}{2} + \log (2 \sqrt{2})

\frac{π}{6} + \log (2 \sqrt{2})

\frac{π}{3} + \log (2 \sqrt{2})

\int \frac{d x}{(x + 1) (x + 2)}

\int (l o g x)^{2} d x =

\int x \sec x^{2} d x is equal to

\frac{1}{2}

\frac{x^{2}}{2}

Join BYJU'S Learning Program