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

1. (a) \(\frac{2}{15}(5x-2)^{\frac{3}{2}}+c\)
2. (b) \(\frac{3}{16}(4x+3)^{\frac{4}{3}}+c\)

\(-12(3x+1)^{-\frac{1}{3}}+c\)

1. (a) \(\frac{1}{4}\sin(4x-1)+c\)
2. (b) \(\frac{5}{2}\sin(2x+3)+c\)

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

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

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

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

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

1. (a) \(2\ln|x^2+7|+c\)
2. (b) \(\ln|x^3+2|+c\)

\(4e^{x^2-3}+c\)

\(4\tan(3x-2)+c\)

1. (a) \(s=-80e^{-0.5t}+80\)
2. (b) \(s=69.2\) cm

1. (a) \(N=300\ln(2t+5)+1000-300\ln 5\)
2. (b) \(N=1480\) bacteria

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

\(f(x)=8\ln(2+\sin x)+1.21\)