Q.Find $\displaystyle\int (x^{5}+4x-7)\,dx$ and verify your answer by differentiation.

Apply the power rule to each term, then differentiate the result to confirm the original expression reappears.

Each term follows the power rule: $\int x^{5}dx=\frac{x^{6}}{6}$, $\int4x\,dx=2x^{2}$, $\int-7\,dx=-7x$.

Integrate term by term using the power-rule formula:

Combining:

Verification by differentiation:

which is exactly the original integrand, confirming the answer.

Integrating the constant term $-7$ as $0$ instead of $-7x$ — a plain constant is $-7x^{0}$, and the power rule still applies with $n=0$, giving $\frac{-7x^{1}}{1}=-7x$, not zero.