Integrate the functions in Exercises 1 to 22. 13. $\tan^{-1} x$
2.
Choose the correct answer in Exercises 24 and 25. 24. $\int \frac{dx}{x^2+2x+2}$ equals
a.
$x \tan^{-1}(x+1) + C$
b.
$\tan^{-1}(x+1) + C$
c.
$(x+1)\tan^{-1}x + C$
d.
$\tan^{-1}x + C$
3.
Find the integrals of the functions in Exercises 1 to 22: 5. $\sin^3 x \cos^3 x$
4.
Choose the correct answer in Exercises 21 and 22. 22. $\int_{0}^{\frac{2}{3}} \frac{dx}{4+9x^2}$ equals
a.
$\frac{\pi}{6}$
b.
$\frac{\pi}{12}$
c.
$\frac{\pi}{24}$
d.
$\frac{\pi}{4}$
5.
Evaluate the definite integrals in Exercises 1 to 20. 3. $\int_{1}^{2} (4x^3 - 5x^2 + 6x + 9) dx$
6.
Integrate the functions in Exercises 1 to 37: 14. $\frac{1}{x(\log x)^m}$, $x > 0, m \neq 1$
7.
Evaluate the definite integrals in Exercises 24 to 31. 31. $\int_{1}^{4} [|x-1|+|x-2|+|x-3|] dx$
8.
Integrate the functions in Exercises 1 to 22. 17. $\frac{x e^x}{(1+x)^2}$
9.
Integrate the functions in Exercises 1 to 37: 26. $\frac{\cos \sqrt{x}}{\sqrt{x}}$
10.
Integrate the functions in Exercises 1 to 22. 3. $x^2 e^x$
11.
Find the integrals of the functions in Exercises 1 to 22: 15. $\tan^3 2x \sec 2x$
12.
Integrate the functions in Exercises 1 to 23. 2. $\frac{1}{\sqrt{x+a} + \sqrt{x+b}}$
13.
Choose the correct answers in Exercises 38 to 40 40. If $f(a+b-x) = f(x)$, then $\int_{a}^{b} x f(x) dx$ is equal to
a.
$\frac{a+b}{2} \int_{a}^{b} f(b-x) dx$
b.
$\frac{a+b}{2} \int_{a}^{b} f(b+x) dx$
c.
$\frac{b-a}{2} \int_{a}^{b} f(x) dx$
d.
$\frac{a+b}{2} \int_{a}^{b} f(x) dx$
14.
Find the following integrals 19. $\int \frac{\sec^2 x}{\csc^2 x} dx$
15.
Integrate the functions in Exercises 1 to 37: 2. $\frac{(\log x)^2}{x}$
16.
Integrate the functions in Exercises 1 to 23. 6. $\frac{x^2}{1-x^6}$
17.
Integrate the functions in Exercises 1 to 37: 34. $\frac{\sqrt{\tan x}}{\sin x \cos x}$
18.
Integrate the rational functions in Exercises 1 to 21. 8. $\frac{x}{(x-1)^2(x+2)}$
19.
Evaluate the definite integrals in Exercises 1 to 20. 2. $\int_{2}^{3} \frac{1}{x} dx$
20.
Integrate the functions in Exercises 1 to 23. 17. $\frac{x+2}{\sqrt{x^2-1}}$
