Further integration: practice Problem set B Answers

\(y=14x^{3/2}+22\)

1. (a) \(f(x)=4\sin x+7\cos x+3\)
2. (b) \(y=5e^x-2\ln x+1-5e\)
3. (c) \(2x^2+3\ln|x|+c\)

1. (a) \(-\frac{1}{40}(2-5x)^{8}+c\)
2. (b) \(-\frac{5}{3}\cos(3x)+\frac{2}{3}\sin(6x)+c\)
3. (c) \(\frac{2}{7}(x^2+2)^{7}+c\)

1. (a) \(\frac{2}{27}(3x^3+7)^{3/2}+c\)
2. (b) \(-\frac{1}{8}(5-3x^2)^{4/3}+c\)

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

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

1. (a) \(y=\frac{1}{8}\sin(4x^2)+c\)
2. (b) \(2\sqrt{3x^2+1}+c\)

1. (a) \(V=0.3t^3+3t+20\)
2. (b) 51.2 cm³

1. (a) \(x=15t-4e^t+34\)
2. (b) 34.4 metres

1. (a) \(f(x)=-\frac{4}{3(3x-2)}+\frac{4}{3}\)
2. (b) \(f(x)=\frac{3}{8}(\ln x)^2+\frac{9}{2}\)

\(f(-7)=2+5\ln\frac{7}{3}\)

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

1. (a) \(\frac{1}{3}(x^2+8)^{3/2}+c\)
2. (b) \(4\ln|\ln x|+c\)

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