JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

\int \frac{f(x)}{x^3-1} d x

, where

f(x)

is a polynomial of degree 2 in

x

such that

f(0)=f(1)=3 f(2)=-3

and

\int \frac{f(x)}{x^3-1} d x=-\log |x-1|+\log \left|x^2+x+1\right|

+\frac{m}{\sqrt{n}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+ C.

Then

(2 m+n)

View answer and explanation

Correct option: C

Option C (7) is correct because after solving the integral and comparing coefficients, we find m=2 and n=3, thus 2m+n=7.

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