Further integration: practice Problem set A Answers

\(y=10x^{3/2}-5\)

1. (a) \(f(x)=6\sin x+5\cos x+4\)
2. (b) \(y=3e^x+4\ln x+2-3e\)
3. (c) \(\frac{3}{2}x^2+\frac{4}{3}\ln|x|+c\)

1. (a) \(-\frac{1}{27}(7-3x)^{9}+c\)
2. (b) \(-\frac{3}{4}\cos(4x)+4\sin(2x)+c\)
3. (c) \(\frac{3}{5}(x^2+3)^{5}+c\)

1. (a) \(\frac{2}{45}(5x^3+2)^{3/2}+c\)
2. (b) \(-\frac{3}{16}(7-2x^2)^{4/3}+c\)

1. (a) \(\frac{3}{4}e^{6x^2}+c\)
2. (b) \(-\frac{4}{3}e^{-2x^3}+c\)

1. (a) \(\frac{1}{6}\ln|2x^3+9|+c\)
2. (b) \(-\frac{1}{4}\ln|1-x^4|+c\)

1. (a) \(y=-\frac{1}{10}\cos(5x^2)+c\)
2. (b) \(2\sqrt{2x^2+9}+c\)

1. (a) \(V=0.2t^3+2t+15\)
2. (b) 50 litres

1. (a) \(x=12t-5e^t+13\)
2. (b) 8.59 metres

1. (a) \(f(x)=-\frac{3}{2(2x+1)}+\frac{1}{2}\)
2. (b) \(f(x)=\frac{5}{4}(\ln x)^2+\frac{7}{4}\)

\(f(-5)=4+3\ln\frac{5}{2}\)

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

1. (a) \(\frac{1}{3}(x^2+5)^{3/2}+c\)
2. (b) \(6\ln|\ln x|+c\)

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