Exam 34: Methods of Integration

Integrate: $\int \log 7 x \cdot d x$

Integrate: $\int_{0}^{\sqrt{5}} \frac{x}{\sqrt{x^{2}+4}} d x$

Find the average ordinate for the function $y=2 x^{2}-x^{3}$ in the interval $x=0$ to $x=2$ . Round your answer to three significant digits.

Integrate by parts: $\int \ln \left(x^{2}+4\right) d x$

Integrate: $\int \sqrt{x^{2}+9} d x$

Evaluate the improper integral: $\int_{3}^{\infty} \frac{d x}{x^{2}-1}$ . Round your answer to three significant digits.

Evaluate the improper integral: $\int_{0}^{4} \frac{d x}{\sqrt{4-x}}$

Integrate: $\int\left(e^{2 x}-e^{-2 x}\right) d x$

Integrate by parts: $\int x^{3} \ln x d x$