Integrating f(ax+b) and by inspection Problem set B Answers

1. (a) \(\frac{2}{9}(3x+7)^{\frac{3}{2}}+c\)
2. (b) \(\frac{3}{8}(2x-5)^{\frac{4}{3}}+c\)

\(-4(5x-2)^{-\frac{1}{2}}+c\)

1. (a) \(\frac{1}{6}\sin(6x+2)+c\)
2. (b) \(2\sin(4x-5)+c\)

1. (a) \(-\frac{1}{5}\cos(5x-1)+c\)
2. (b) \(3\cos(2-3x)+c\)

1. (a) \(2e^{3x-2}+c\)
2. (b) \(-4e^{4-3x}+c\)

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

\(\frac{5}{4}(x^2+4)^{4}+c\)

1. (a) \(2\sin^{3}x+c\)
2. (b) \(-\frac{1}{6}\cos^{6}x+c\)

1. (a) \(3\ln|x^2+2|+c\)
2. (b) \(\ln|x^4+9|+c\)

\(3e^{x^3+2}+c\)

\(3\tan(5x+1)+c\)

1. (a) \(V=-100e^{-0.3t}+100\)
2. (b) \(V=83.5\) litres

1. (a) \(V=150\ln(3t+2)+500-150\ln 2\)
2. (b) \(V=885\) visitors

\(\frac{4}{3}(x^3+1)^{\frac{3}{2}}+c\)

\(f(x)=6\ln(3-\cos x)-3.32\)