jee-main 2016 Q88

jee-main · India · 09apr Integration by Substitution Substitution to Compute an Indefinite Integral with Initial Condition

If $m$ is a non-zero number and $\int \frac{x^{5m-1} + 2x^{4m-1}}{(x^{2m} + x^m + 1)^3} dx = f(x) + C$, then $f(x)$ is:
(1) $\frac{x^{5m}}{2m(x^{2m} + x^m + 1)^2}$
(2) $\frac{x^{4m}}{2m(x^{2m} + x^m + 1)^2}$
(3) $\frac{(2x^{2m} + x^m)}{(x^{2m} + x^m + 1)^2}$
(4) $\frac{(x^{5m} + x^{4m})}{2m(x^{2m} + x^m + 1)^2}$

If $m$ is a non-zero number and $\int \frac{x^{5m-1} + 2x^{4m-1}}{(x^{2m} + x^m + 1)^3} dx = f(x) + C$, then $f(x)$ is:\\
(1) $\frac{x^{5m}}{2m(x^{2m} + x^m + 1)^2}$\\
(2) $\frac{x^{4m}}{2m(x^{2m} + x^m + 1)^2}$\\
(3) $\frac{(2x^{2m} + x^m)}{(x^{2m} + x^m + 1)^2}$\\
(4) $\frac{(x^{5m} + x^{4m})}{2m(x^{2m} + x^m + 1)^2}$

Paper Questions

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