2x (1+x^2) 1+x^2 dx:

MCQ

$\int\frac{2\text{x}\log(1+\text{x}^2)}{1+\text{x}^2}\text{dx:}$

A
$\log(1+\text{x}^2)+\text{c}$
✓
$\frac{[\log(1+\text{x}^2)^2]}{2}+\text{c}$
C
$2\log(1+\text{x}^2)+\text{c}$
D
None of these

✓

Answer

Correct option: B.

$\frac{[\log(1+\text{x}^2)^2]}{2}+\text{c}$

$\int\frac{2\text{x}\log(1+\text{x}^2)}{1+\text{x}^2}\text{dx}$

Let $\log(1+\text{x}^2) =\text{z}$ and $\frac{\text{2x}}{1+\text{x}^2}\text{dx}=\text{dz}$ Using these in the above integration we get,

$=\int\text{z, }{\text{dz}}$

$\frac{\text{z}^2}{2}+\text{c}$ [Where c is integrating constant]

$=\frac{[\log(1+\text{x}^2)^2]}{2}+\text{c}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

INTEGRALS — Maths STD 12 Science — Question

Answer

Need a full question paper?

Explore more

Similar questions