Integrating powers and standard functions Problem set A Answers

\(\frac{3}{8}x^{\frac{8}{3}} + c\)

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

\(\frac{27}{4}x^{\frac{4}{3}} + c\)

\(\frac{9}{20}x^{\frac{4}{3}} + c\)

\(9x^{\frac{2}{3}} + c\)

1. (a) \(y=5\sin x+c\)
2. (b) \(y=-3\cos x+c\)

\(y=6e^x+4\)

\(y=8\ln x+3\)

\(y=-4\cos x-e^x+5x+c\)

1. (a) \(h=6t^{\frac{1}{2}}-4\)
2. (b) \(h=14\) m

1. (a) \(s=-6e^{-2t}+6\)
2. (b) \(s=5.70\) m

\(y=2x^{\frac{5}{2}}-4\ln x+4x^{\frac{1}{2}}-46.5\)

\(x+12\sqrt{x}+9\ln|x|+c\)