Exam 34: Methods of Integration

Integrate: $\int_{}^{}\left(e^{2 x}+x e^{x^{2}}\right) \cdot dx$

Integrate: $\int \frac{d x}{\sqrt{x}-\sqrt[4]{x}}$

Integrate: $\int_{\frac{1}{4}}^{1} \ln 4 x d x$

Integrate: $\int_{-2}^{1} \frac{-4}{x^{2}+x-6} d x$ . Round your answer to three significant digits.

Evaluate the integral using Simpson's rule. Choose 10 panels of equal width: $\int_1^6 \frac{dx}{x^{2}+1}$ . Round your answer to three significant digits.

Integrate by parts: $\int 4 x^{2} e^{2 x} d x$

Find the rms value for the function in the given interval: $y=2 \sin 3 x$ from $x=0$ to $x=\frac{\pi}{3}$ . Round your answer to three significant digits.

Integrate: $\int \frac{2 x+4}{x^{3}-2 x^{2}} d x$

Integrate: $\int \sqrt{1+e^{x}} d x$

Integrate: $\int 4^{5 x} d x$

Integrate: $\int \frac{d x}{\sqrt{4-x^{2}}}$

Integrate: $\int \frac{x^{2} d x}{\sqrt{x^{2}+4}}$

Integrate: $\int \csc 2 x d x$

Evaluate: $\int_{0}^{\pi / 2} \cos x e^{\sin x} d x$ . Round your answer to three significant digits.

Integrate: $\int x^{2} \sqrt{x^{2}+1} d x$

Integrate: $\int(10 x-5) \ln \left(x^{2}-x\right) d x$

Find the area bounded by the curve $y=2 \tan \frac{x}{4}$ and the $x$ -axis from $x=0$ to $x=\pi$ .

Integrate: $\int 3 x^{2} e^{x^{3}} d x$

Integrate: $\int 4 \log 2 x d x$

Find the rms value for the function in the given interval: $y=5 e^{-3 t}$ from $t=0$ to $t=1.5$