Integration and Differentiation Practice Questions

Stage: 5 Challenge Level:
Differentiation:

1. $8 e^x + (8x+7) e^x$
2. $\displaystyle\frac{12x+2}{6x^2+2x+5}$
3. $(-10x-8)\cos(5x^2+8x-2)$
4. $(-14x-5)\cos x + (7x^2+5x) \sin x$
5. $\left( 2x-8 \right) e^{x^2-8x+7}$
6. $(8x+3) \ln x + \displaystyle\frac{4x^2+3x+7}{x}$

Integration:

1. $\frac{1}{4}\left( x+9 \right)^4$
2. $-\cos x \ln(\cos x)+\cos x + c$
3. $\frac{2}{3}(1+x^2)^{3/2}+c$
4. $-e^{\cos x}+c$
5. $-x^2 \cos x + 2x \sin x + 2 \cos x + c$
6. $\frac{1}{2}e^x (\cos x + \sin x) + c$