Mathematics - Indefinite Integration Question with Solution | TestHub

Let $I=\int \frac{(6x^4-\left(x^4-1\right)dx}{3x^{4/3}\sqrt{x^4-1}}=\int \left(\frac{2x^{8/3}}{\sqrt{x^4-1}}-\frac{\sqrt{x^4-1}}{3x^{4/3}}\right)=\int \frac{d}{dx}\left(\frac{\sqrt{x^4-1}}{x^{1/3}}\right)dx=\frac{\sqrt{x^4-1}}{x^{1/3}}+C$ $\Rightarrow \frac{1}{\mathrm{m}}=3\Rightarrow \frac{3}{\mathrm{m}}=9$

Aliter :

Differentiate both sides to get ƒ(x).