1. $\int 3x e^{-x} dx = -3e^{-x}(x + 1) + C$
2. $\int \frac{\ln x}{x^2} dx = -\frac{\ln x}{x} - \frac{1}{x} + C$
3. $\int x^2 \cos x dx = x^2 \sin x + 2x \cos x - 2 \sin x + C$
4. $\int x \sin x \cos x dx = \frac{x \sin(2x)}{4} + \frac{\cos(2x)}{8} + C$
5. $\int \cos^{-1} x dx = x \cos^{-1} x - \sqrt{1 - x^2} + C$
6. $\int (\ln x)^2 dx = x(\ln x)^2 - 2x \ln x + 2x + C$
7. $\int x^3 \sqrt{9 - x^2} dx = -\frac{(9 - x^2)^{3/2}}{15}(3x^2 + 18) + C$
8. $\int e^{2x} \sin x dx = \frac{e^{2x}}{5}(2 \sin x - \cos x) + C$
9. $\int x^2 \sqrt{x - 1} dx = \frac{2(x - 1)^{3/2}}{105}(15x^2 + 12x + 8) + C$
10. $\int \frac{1}{x(\ln x)^3} dx = -\frac{1}{2(\ln x)^2} + C$
Parent Tip: Review the logic above to help your child master the concept of integration by parts worksheet.
