Integration by substitution Problem set B Answers

1. (a) \(\tfrac17\sin 7x+c\)
2. (b) \(-\tfrac15\ln|4-5x|+c\)
3. (c) \(\tfrac12e^{3+2x}+c\)

1. (a) \(\ln(6+e^x)+c\)
2. (b) \(\tfrac14\ln|2+x^4|+c\)

1. (a) \(\tfrac13(x^2+11)^{3/2}+c\)
2. (b) \(\tfrac23(1+\sin x)^{3/2}+c\)

1. (a) \(-2e^{-\sqrt x}+c\)
2. (b) \(\ln|1+\ln x|+c\)

1. (a) \(-\tfrac18\cos 8x+c\)
2. (b) \(-\tfrac14e^{-4x}+c\)
3. (c) \(\tfrac15\ln|2+5x|+c\)
4. (d) \(-\ln|9-x|+c\)

1. (a) \(\tfrac18e^{x^8}+c\)
2. (b) \(\tfrac14\sin(x^4)+c\)
3. (c) \(\tfrac18\ln(5+4x^2)+c\)
4. (d) \(-\ln(3+\cos x)+c\)

1. (a) \(-\tfrac14\cos^4x+c\)
2. (b) \(-\tfrac13\ln|\cos 3x|+c\)

\(\frac{61}{3}=20.3\) litres

2.05 mg per litre

\(\ln\frac{5+e^2}{6}=0.725\) m²

\(\frac25(x+5)^{5/2}-\frac{10}{3}(x+5)^{3/2}+c\)

\(\frac{\pi}{4}=0.785\)