Calculus 2: Strategy for integration

Evaluate the integral $8 \displaystyle \int_{1}^{\frac{\sqrt{5}}{2}} u^2 \, du$.

Evaluate the integral from 0 to 2 of $\displaystyle \int_{0}^{2} (5x^4 - 2x) \, dx$ using the fundamental theorem of calculus Part 2.

Evaluate $\displaystyle \int \frac{1}{(x^2 + 1)^2} \, dx$ using an appropriate substitution method.

Evaluate $\displaystyle \int_{0}^{3} e^{2x} \, dx$ using the $u$-substitution method, where $u = 2x$.

Evaluate the integral $\displaystyle \int \left( e^x \, \cdot \, \sqrt{e^{2x} - 4}\right) \, dx$ using substitution.

Find the integral $\displaystyle \int \frac{\sqrt{t^2 + 2t}}{t + 1} \, dt$.

Simplify and integrate $\displaystyle \int \frac{4}{x^2 - 2x - 8} \, dx$ by completing the square.

Make the substitution $u = e^x$ to evaluate the integral $\int \frac{du}{u^2 \sqrt{9 - u^2}}$.

Evaluate the integral $\displaystyle \int_{1}^{4} \frac{1}{(4-x)^{2/3}} \, dx$.