If $\smallint \,\,\frac{{x + 2}}{{2{x^2} + \,\,6x\,\, + 5}}\,\,dx = P\,\,\smallint \,\,\frac{{4x + 6}}{{2{x^2} + \,\,6x\,\, + 5}}\,\,dx\,\, + \,\,\frac{1}{2}\smallint \,\,\frac{{dx}}{{2{x^2} + \,\,6x\,\, + 5}}$ , then the value of $P$ is

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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\int \,\,\frac{{x + 2}}{{2{x^2} + \,\,6x\,\, + 5}}\,\,dx = P\,\,\int \,\,\frac{{4x + 6}}{{2{x^2} + \,\,6x\,\, + 5}}\,\,dx\,\, + \,\,\frac{1}{2}\int \,\,\frac{{dx}}{{2{x^2} + \,\,6x\,\, + 5}}

, then the value of

P

View answer and explanation

Correct option: C

\frac{1}{4}

Option C (

\frac{1}{4}

) is correct because by manipulating the integral, we can find that P equals

\frac{1}{4}