Math 3112 - Worksheet 1
Techniques of Integration

1.

$$\int t e^{t^2}\ dt$$

2.

$$\int t e^{2t}\ dt$$

3.

$$\int \ln 3x\ dx$$

4.

$$\int \frac{dx}{\sqrt{1-x}}$$

5.

$$\int t^2 \sin t\ dt$$

6.

$$\int \theta \sec (2\theta^2)\ d \theta$$

7.

$$\int \sin^2 x\ dx$$

8.

$$\int \tan \alpha\ d\alpha$$

9.

$$\int \sin^8 x \cos^5 x \ dx$$

10.

$$\int e^x \cos 2x\ dx$$

11.

$$\int x^7 \ln 2x\ dx$$

12.

$$\int \sin 3x \cos 4x\ dx$$

13.

$$\int \cos^5 x\ dx$$

14.

$$\int \sin^4 x\ dx$$

15.

$$\int \sec^3 3\phi\ d\phi$$

16.

$$\int \sec^4 3\phi\ d\phi$$

17.

$$\int \sqrt{4+7t}\,dt$$

18.

$$\int \sqrt{4+7t^2}\,dt$$

19.

$$\int \sqrt{1-6t^2}\,dt$$

20.

$$\int e^{-t^2}\ dt$$

21.

$$\int t^2 \sqrt[3]{1-7t^3}\,dt$$

22.

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

23.

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

24.

$$\int \frac{dx}{1-x^2}$$

25.

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

26.

$$\int \frac{4t+1}{t^2+t-2}\, dt$$

27.

$$\int \frac{u^2+11}{u^2+4u+5}\, du$$