$\smallint \,\,\frac{{10\,\,{x^9} + \,\,{{10}^x}\,\,{{\log }_e}10}}{{{{10}^x} + {x^{10}}}}\,\,dx$ is equal to

${10^x}\,\, - \,\,{x^{10}} + \,\,c$

${10^x}\,\, + \,\,{x^{10}} + \,\,c$

${\left( {{{10}^x}\,\, - \,\,{x^{10}}} \right)^{ - 1}} + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Understanding +4 | -1

\int \,\,\frac{{10\,\,{x^9} + \,\,{{10}^x}\,\,{{\log }_e}10}}{{{{10}^x} + {x^{10}}}}\,\,dx

is equal to

View answer and explanation

Correct option: D

\log \,\,\left( {{{10}^x}\,\, + \,\,{x^{10}}} \right)\,\, + \,\,c

Option D is correct because the integral can be solved by recognizing the numerator as the derivative of the denominator, leading to a logarithmic solution.

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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