$\smallint \,\,\frac{{m{x^{m + 2n - 1}}\,\, - \,\,n{x^{n - 1}}}}{{{x^{2m + 2n}}\,\, + \,\,2{x^{m + n}}\,\, + \,\,1}}\;\,\,dx$ is equal to

$\frac{{{x^m}}}{{{x^{m + n}}\,\, + \,\,1}}\,\, + \,\,c$

$\frac{{{x^{m + n}}\,\, - \,\,1}}{{{x^{m + n}}\,\, + \,\,1}}\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

\int \,\,\frac{{m{x^{m + 2n - 1}}\,\, - \,\,n{x^{n - 1}}}}{{{x^{2m + 2n}}\,\, + \,\,2{x^{m + n}}\,\, + \,\,1}}\;\,\,dx

is equal to

View answer and explanation

Correct option: D

- \,\,\frac{{{x^n}}}{{{x^{m + n}}\,\, + \,\,1}}\,\, + \,\,c

Option D (

- \,\frac{{{x^n}}}{{{{x^{m + n}}\\ + \\,1}}}\\ + \\,c

) is correct because it is the result of the integration after appropriate substitution and simplification.