If $\smallint \,\,\frac{1}{{x + {x^5}}}\,\,dx = f\left( x \right) + c$, then the value of $\smallint \frac{{{x^4}}}{{x + {x^5}}}\,\;dx$ equals

$f\left( x \right)\,\, + \,\,\log \,\,x\,\, + \,\,c$

$f\left( x \right)\,\, - \,\,\log \,\,x\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{1}{{x + {x^5}}}\,\,dx = f\left( x \right) + c

, then the value of

\int \frac{{{x^4}}}{{x + {x^5}}}\,\;dx

equals

View answer and explanation

Correct option: A

\log \,\,x\,\, - \,\,f\,\,\left( x \right)\,\, + \,\,c

Option A (

\log \,\,x\,\, - \,\,f\,\,\left( x \right)\,\, + \,\,c

) is correct because it is obtained by manipulating the integrand and using the given integral.