MCQ
$\int {\frac{{\cos x + x\sin x}}{{x(x - \cos x)}}dx = } $
  • A
    $\log |x(x - \cos x)| + c$
  • $\log \left| {1 - \frac{{\cos x}}{x}} \right| + c$
  • C
    $\log \left| {\frac{x}{{x - \cos x}}} \right| + c$
  • D
    None of these

Answer

Correct option: B.
$\log \left| {1 - \frac{{\cos x}}{x}} \right| + c$
b
$\int \frac{\cos x+x \sin x}{x^{2}\left(1-\frac{\cos x}{x}\right)} \cdot d x$

Put $1-\frac{\cos x}{x}=t$

$-\left[\frac{-x \sin x-\cos x}{x^{2}}\right] d x=d t$

$\frac{x \sin x+\cos x}{x^{2}} d x=d t$

$\int \frac{\mathrm{dt}}{\mathrm{t}}$

$\ln t+c$

$ = \ln \left| {1 - \frac{{\cos {\rm{x}}}}{{\rm{x}}}} \right| + {\rm{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

Similar questions

$\int\frac{\cos2\text{x dx}}{(\sin\text{x}+\cos\text{x})^2}=$
Let $f (x) =$  $\left[ {\begin{array}{*{20}{c}}  {\begin{array}{*{20}{c}}  {\frac{{\begin{array}{*{20}{c}}  {{2^x}}&{ + {2^{3 - x}}}&{ - 6} \end{array}}}{{\begin{array}{*{20}{c}}  {\sqrt {{2^{ - x}}} }&{ - {2^{1 - x}}} \end{array}}}}&{if}&{x > 2} \end{array}} \\   {} \\   {} \\   {} \\   {\begin{array}{*{20}{c}}   {\frac{{\begin{array}{*{20}{c}}  {{x^2}}&{ - 4} \end{array}}}{{x - \sqrt {3x - 2} }}}&{if}&{x < 2}  \end{array}} \end{array}} \right.$  then
$\int_{}^{} {{x^3}{e^{{x^2}}}dx = } $
What is the length of the longer diagonal of the parallelogram constructed on $5\vec{\text{a}}+2\vec{\text{b}}$ and $\vec{\text{a}}-3\vec{\text{b}}$ if it is given that $|\vec{\text{a}}|=2\sqrt{2},\big|\vec{\text{b}}\big|=3$ and the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$ is $\frac{\pi}{4}$?
If $\left| {\begin{array}{*{20}{c}}
  {\cos 2x}&{{{\sin }^2}x}&{\cos 4x} \\ 
  {{{\sin }^2}x}&{\cos 2x}&{{{\cos }^2}x} \\ 
  {\cos 4x}&{{{\cos }^2}x}&{\cos 2x} 
\end{array}} \right| = {a_0} + {a_1}\sin x + {a_2}{\sin ^2}x + .....$ then $a_0$ is equal to
$\int\frac{\text{x}^9}{(4\text{x}^2+1)^6}\text{dx}$ is equal to:
A solution of the differential equation ${\left( {\frac{{dy}}{{dx}}} \right)^2} - x\frac{{dy}}{{dx}} + y = 0$ is
The value of $\int_{\,0}^{\,1} {\,\frac{{dx}}{{x + \sqrt {1 - {x^2}} }}} $ is
The value of $\int_0^{\pi /2} {\frac{{\sin x}}{{1 + {{\cos }^2}x}}\,dx} $ is
Line passing through (3, 4, 5) and (4, 5, 6) has direction ratios: