Test 2

1.  Evaluate the integral

${\int }_0^4\frac{x}{x+9}dx$

2. Evaluate the integral

$\int \frac{x–1}{x^2+2x}dx$

3.  Use table of integrals to evaluate the integral

${\int }_3^6\frac{1}{2x^3–3x^2}dx$

4.   Use table of integrals to evaluate the integral

$\int \frac{e^x}{4–e^{2x}}dx$

5.  Evaluate the integral

${\int }_0^1\frac{dx}{x^{0.2}}$

6. Use long division to evaluate the integral.

$\int \frac{x^2}{x+2}dx$

7. Evaluate the integral

$\int \frac{\sin 2x}{1+{\cos }^{4}x}dx$

8.  Evaluate the integral

$\int \frac{x^2+x+1}{{(x^2+1)}^2}dx$

9. Evaluate the integral

${\int }_{\mathrm{\pi }/3}^{\mathrm{\pi }/2}{\sin }^{3}x{\cos }^{4}xdx$

10.  Using trigonometric substitution evaluate the integral.

${\int }_0^{2/3}\sqrt{4–9x^{2}dx}$

11. Evaluate

${\int }_0^{\mathrm{\pi }/3}({\tan }^2\theta + {\tan }^4\theta ) d\theta$

12 Evaluate

${\int }_0^1(y^2+1)e^{–y}dy$

13.  Evaluate the integral

${\int }_0^{1/2}arc\tan ( 2y ) dy$

14.  Evaluate the integral or show that it is divergent

${\int }_{–\infty }^{\infty }\frac{dx}{4x^2+4x+5}$

15. Evaluate the integral or show that it is divergent

${\int }_{0.5}^1\frac{1}{\sqrt{1–u^2}}du$

16.  Evaluate the integral

${\int }_0^{1/2}x\mathrm{cos\pi }xdx$

17.  Evaluate the integral

${\int }_{\mathrm{\pi }/4}^{\mathrm{\pi }/2}co{t}^{3}xdx$

18.Evaluate the integral

${\int }_2^3\frac{x(3–5x)}{(3x–1) {(x–1)}^2}dx$

19.  Evaluate the indefinite integral

$\int x\cos 7xdx$

20.  Evaluate the integral 

${\int }_{\mathrm{\pi }/6}^{\mathrm{\pi }/2}{\tan }^2\theta {\cos }^3\theta d\theta$