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Mathematics LibreTexts

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)