These problems require the techniques of this chapter, and are in no particular order. Some problems may be done in more than one way.

Exercises 8.7

Ex 8.7.1 $\ds\int (t+4)^3\,dt$ (answer)

Ex 8.7.2 $\ds\int t(t^2-9)^{3/2}\,dt$ (answer)

Ex 8.7.3 $\ds\int (e^{t^2}+16)te^{t^2}\,dt$ (answer)

Ex 8.7.4 $\ds\int \sin t\cos 2t\,dt$ (answer)

Ex 8.7.5 $\ds\int \tan t\sec^2t\,dt$ (answer)

Ex 8.7.6 $\ds\int {2t+1\over t^2+t+3}\,dt$ (answer)

Ex 8.7.7 $\ds\int {1\over t(t^2-4)}\,dt$ (answer)

Ex 8.7.8 $\ds\int {1\over (25-t^2)^{3/2}}\,dt$ (answer)

Ex 8.7.9 $\ds\int {\cos 3t\over\sqrt{\sin3t}}\,dt$ (answer)

Ex 8.7.10 $\ds\int t\sec^2 t\,dt$ (answer)

Ex 8.7.11 $\ds\int {e^t\over \sqrt{e^t+1}}\,dt$ (answer)

Ex 8.7.12 $\ds\int \cos^4 t\,dt$ (answer)

Ex 8.7.13 $\ds\int {1\over t^2+3t}\,dt$ (answer)

Ex 8.7.14 $\ds\int {1\over t^2\sqrt{1+t^2}}\,dt$ (answer)

Ex 8.7.15 $\ds\int {\sec^2t\over (1+\tan t)^3}\,dt$ (answer)

Ex 8.7.16 $\ds\int t^3\sqrt{t^2+1}\,dt$ (answer)

Ex 8.7.17 $\ds\int e^t\sin t\,dt$ (answer)

Ex 8.7.18 $\ds\int (t^{3/2}+47)^3\sqrt{t}\,dt$ (answer)

Ex 8.7.19 $\ds\int {t^3\over (2-t^2)^{5/2}}\,dt$ (answer)

Ex 8.7.20 $\ds\int {1\over t(9+4t^2)}\,dt$ (answer)

Ex 8.7.21 $\ds\int {\arctan 2t\over 1+4t^2}\,dt$ (answer)

Ex 8.7.22 $\ds\int {t\over t^2+2t-3}\,dt$ (answer)

Ex 8.7.23 $\ds\int \sin^3 t\cos^4 t\,dt$ (answer)

Ex 8.7.24 $\ds\int {1\over t^2-6t+9}\,dt$ (answer)

Ex 8.7.25 $\ds\int {1\over t(\ln t)^2}\,dt$ (answer)

Ex 8.7.26 $\ds\int t(\ln t)^2\,dt$ (answer)

Ex 8.7.27 $\ds\int t^3e^{t}\,dt$ (answer)

Ex 8.7.28 $\ds\int {t+1\over t^2+t-1}\,dt$ (answer)