Evaluate $\int \left(3 x^{2} + 4 x - 5\right)\,dx$.

Explanation

1. 01

   Integrate term by term with the standard forms: $\int x^n\,dx = \frac{x^{n+1}}{n+1}$, $\int \frac{1}{x}\,dx = \log|x|$, $\int e^x\,dx = e^x$.

2. 02

   $\int \left(3 x^{2} + 4 x - 5\right)\,dx = x^{3} + 2 x^{2} - 5 x + C$.

3. 03

   Check: differentiating the answer gives back the integrand.