Mathematics

The integral $$\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx$$ is equal to?(Here C is a constant of integration)


ANSWER

$$\log_e\left|\dfrac{x^3+1}{x}\right|+C$$


SOLUTION
$$\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx$$

$$\displaystyle\int \dfrac{2x-\dfrac{1}{x^2}}{x^2+\dfrac{1}{x}}dx$$

$$x^2+\dfrac{1}{x}=t$$

$$\left(2x-\dfrac{1}{x^2}\right)dx=dt$$

$$\displaystyle\int \dfrac{dt}{t}=ln (t)+C$$

$$=ln \left(x^2+\dfrac{1}{x}\right)+C$$
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Single Correct Medium Published on 17th 09, 2020
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