The correct option is A log| x x+1 | +c ∫ dx x( x+1 ) nbsp; nbsp; =∫ 1 x dx ∫ 1 x+1 dx nbsp; nbsp; nbsp; nbsp; nbsp; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Property 2

Solve ∫ dx ...

Question

Solve $\int \frac{d x}{x (x + 1)}$

log ∣ ∣ ∣ \frac{x + 1}{x} ∣ ∣ ∣ + c

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

log ∣ ∣ ∣ \frac{x}{x + 1} ∣ ∣ ∣ + c

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

log ∣ ∣ ∣ \frac{x - 1}{x} ∣ ∣ ∣ + c

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

log ∣ ∣ ∣ \frac{x - 1}{x + 1} ∣ ∣ ∣ + c

where

c

is an arbitrary constant

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

Open in App

Solution

The correct option is A $log ∣ ∣ ∣ \frac{x}{x + 1} ∣ ∣ ∣ + c$
$\int \frac{d x}{x (x + 1)} = \int \frac{1}{x} d x - \int \frac{1}{x + 1} d x$
$= log x - log (x + 1) + c$
$= log ∣ ∣ ∣ \frac{x}{x + 1} ∣ ∣ ∣ + c$

Suggest Corrections

Similar questions

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

f (\frac{x - 4}{x + 2}) = 2 x + 1, (x \in R - {1, - 2}),

\int f (x) d x

C

\int \frac{d x}{(x + 1) (x - 2)} = A log (x + 1) + B log (x - 2) + C

\int \frac{x dx}{(x - 1) (x^{2} + 4)}

\int \frac{1}{1 - \cos x - \sin x} d x =

\log |1 + \cot \frac{x}{2}| + C

\log |1 - \tan \frac{x}{2}| + C

\log |1 - \cot \frac{x}{2}| + C

\log |1 + \tan \frac{x}{2}| + C

Join BYJU'S Learning Program