Integration by substitution Problem set A Answers

1. (a) \(-\tfrac19\cos 9x+c\)
2. (b) \(-\tfrac13\ln|7-3x|+c\)
3. (c) \(\tfrac15e^{2+5x}+c\)

1. (a) \(\ln(4+e^x)+c\)
2. (b) \(\tfrac13\ln|5+x^3|+c\)

1. (a) \(\tfrac13(x^2+7)^{3/2}+c\)
2. (b) \(-\tfrac23\cos^{3/2}x+c\)

1. (a) \(2\sin\sqrt x+c\)
2. (b) \(-\cos(\ln x)+c\)

1. (a) \(\tfrac16\sin 6x+c\)
2. (b) \(-\tfrac12e^{-2x}+c\)
3. (c) \(\tfrac12\ln|5+2x|+c\)
4. (d) \(-\ln|6-x|+c\)

1. (a) \(\tfrac14e^{x^4}+c\)
2. (b) \(-\tfrac16\cos(x^6)+c\)
3. (c) \(\tfrac14\ln(3+2x^2)+c\)
4. (d) \(\ln(4+\sin x)+c\)

1. (a) \(\tfrac14\sin^4x+c\)
2. (b) \(-\tfrac12\ln|\cos 2x|+c\)

\(\frac{98}{3}=32.7\) m

58.9 °C

\(\frac12\ln2=0.347\) m²

\(\frac25(x+3)^{5/2}-2(x+3)^{3/2}+c\)

\(\frac{\pi}{3}=1.05\)