Mathematics

The integral $$\int \dfrac {2x^{12} + 5x^{9}}{(x^{5} + x^{3} + 1)^{3}} dx$$ is equal to:


ANSWER

$$\dfrac {x^{10}}{2(x^{5} + x^{3} + 1)^{2}} + C$$


SOLUTION
$$\int \dfrac {2x^{12} + 5x^{9}}{(x^{5} + x^{3} + 1)^{3}} dx$$
$$=\int \dfrac {2x^{12} + 5x^{9}}{x^{15}(x^{-5} + x^{-2} + 1)^{3}} dx $$
$$=\int \dfrac {2x^{-3} + 5x^{-6}}{(x^{-5} + x^{-2} + 1)^{3}} dx$$

Let $$x^{-5}+x^{-2}+1 =t$$

$$\Rightarrow \int \dfrac{-dt}{t^3}= \dfrac{1}{2t^2}+c$$

$$=\dfrac {x^{10}}{2(x^{5} + x^{3} + 1)^{2}} +c$$
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Single Correct Hard Published on 17th 09, 2020
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