$\smallint \,\,\frac{{x\,\, + \,\,\sin \,\,x}}{{1\,\, + \,\,\cos \,\,x}}\,\,dx$ is equal to

$\log \,\,\left( {1\,\, + \,\,\cos \,\,x} \right)\,\, + \,\,c$

$\cot \,\,\frac{x}{2}\,\, + \,\,c$

$\log \,\,\left( {x\,\, + \,\,\sin \,\,x} \right)\,\, + \,\,c$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

\int \,\,\frac{{x\,\, + \,\,\sin \,\,x}}{{1\,\, + \,\,\cos \,\,x}}\,\,dx

is equal to

View answer and explanation

Correct option: A

x\,\,\tan \,\,\frac{x}{2}\,\, + \,\,c

Option A (

x \tan \frac{x}{2} + c

) is correct because the integral can be solved by rewriting the integrand using trigonometric identities and then integrating by parts.

Practice All Chapter MCQs →

\int \nolimits_0^\infty \,\,\log \,\,\left( {x + \frac{1}{x}} \right)\,\,\frac{{dx}}{{1 + {x^2}}}

f\left( x \right)

\int \nolimits_0^{{t^2}} \,\,x\;\,f\left( x \right)\,\,dx = \frac{2}{5}\,\,{t^5}

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

\int\limits_{{0}}^{11}[x]^{3} . \mathrm{dx}

[*]

\int\limits_{2}^4 \frac{\log x^2}{\log x^2+\log \left(36-12 x+x^2\right)} d x

\int\limits_{{-2}}^0\left(x^3+3 x^2+3 x+3+(x+1) \cos (x+1)\right) d x

I\,\,\left( {m,\,\,n} \right) = \int \nolimits_0^1 \,\,{t^m}\,\,{\left( {1 + t} \right)^n}\,\,dt

I\left( {m,\,\,n} \right)

I\,\,\left( {m + 1,\,\,n + 1} \right)