JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Medium

1 of 1

Analyzing +4 | -1

\int \frac{d x}{\left(x^{2}-2 x+10\right)^{2}}=A\left(\tan ^{-1}\left(\frac{x-1}{3}\right)+\frac{f(x)}{x^{2}-2 x+10}\right)+C

where

\mathrm{C}

is a constant of integration then :

View answer and explanation

Correct option: B

A=\frac{1}{54}

and

f(x)=3(x-1)

Option B (

A=\frac{{1}}{{54}}

and

f(x)=3(x-1)

) is correct because after solving the integral using trigonometric substitution, the result matches the given form with the specified values for A and f(x).

More Questions from INDEFINITE INTEGRATION

Practice All Chapter MCQs →

\int \sin ^5 x \cos ^4 x d x=

f(x)

is differentibale and

\int\limits_{0}^{t^2} x f(x) d x=\frac{2}{5} t^5

then

f\left(\frac{4}{25}\right)

equals If

\int \frac{1-7 \cos ^2 x}{\sin ^7 x \cos ^2 x} d x=\frac{f(x)}{\sin ^7 x}+C

is equal to If

\int {e}^{{x}^2}\left(2-\frac{1}{{x}^2}\right) {de}={e}^{{x}^2} {f}({x})+{C}

and

{f}\left(\frac{1}{2}\right)=2

, then

f(1)

is equal to (where

{C}

is an arbitrary constant)

\int \frac{x^7}{\left(1-x^2\right)^5} d x

is equal to:

\int \,\frac{{a{x^3} + \,\,b{x^2} + c}}{{{x^4}}}\;\,dx

equals