jee-main 2016 Q85

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

The integral $\int \frac{2x^{12} + 5x^9}{(x^5 + x^3 + 1)^3} dx$ is equal to:
(1) $\frac{-x^{10}}{2(x^5 + x^3 + 1)^2} + C$
(2) $\frac{x^{10}}{2(x^5 + x^3 + 1)^2} + C$
(3) $\frac{-x^5}{(x^5 + x^3 + 1)^2} + C$
(4) $\frac{x^5}{2(x^5 + x^3 + 1)^2} + C$

The integral $\int \frac{2x^{12} + 5x^9}{(x^5 + x^3 + 1)^3} dx$ is equal to:\\
(1) $\frac{-x^{10}}{2(x^5 + x^3 + 1)^2} + C$\\
(2) $\frac{x^{10}}{2(x^5 + x^3 + 1)^2} + C$\\
(3) $\frac{-x^5}{(x^5 + x^3 + 1)^2} + C$\\
(4) $\frac{x^5}{2(x^5 + x^3 + 1)^2} + C$

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