$\int\frac{x^3-1}{x^2}dx$ is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{x^2}{2}+\frac{1}{x}+c$, where c is constant of integration
Given:
$\displaystyle \int \frac{x^{3}-1}{x^{2}}\,dx$
Simplify the integrand:
$\frac{x^{3}-1}{x^{2}}=x-\frac{1}{x^{2}}$
Integrate termwise:
$\int x\,dx-\int x^{-2}\,dx$
$=\frac{x^{2}}{2}+\frac{1}{x}+C$
Final answer: $\frac{x^{2}}{2}+\frac{1}{x}+C$