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Mathematics LibreTexts

8.7: Additional exercises

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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