Final Answer:
1. $\frac{2}{3}(4x - 1)^{3/2} + C$
2. $\frac{1}{6}(5x + 2)^6 + C$
3. $-\frac{1}{2}e^{-x^2} + C$
4. $\frac{1}{2}\sin(2\theta + 1) + C$
5. $x e^{x^2} - \frac{1}{2}e^{x^2} + C$
6. $\frac{1}{2}\sin(x^2) + C$
7. $-\frac{1}{3}\sqrt{2 - y^3} + C$
8. $2\sqrt{1 + \cos y} + C$
9. $-\frac{1}{3}y^3 + C$
10. $\tan t + C$
11. $\frac{2}{3}(1 + x^3)^{3/2} + C$
12. $\frac{1}{4}(x^2 + 4)^2 + C$
13. $-\frac{1}{5}\cos(5\theta) + C$
14. $-\frac{1}{2}\cos(x^2 + 2x + 3) + C$
15. $\ln|4 + \frac{x}{2}| + C$ or $\ln|x + 8| + C$ (up to constant)
16. $\frac{1}{9}\sin(9\theta) + C$
17. $\frac{1}{2}x\sqrt{x^2 + 4} + 2\ln\left|x + \sqrt{x^2 + 4}\right| + C$
18. $-\cos x \sqrt{\sin x} + C$
19. $\frac{1}{3}(y^2 + 1)^{3/2} + C$
20. $\frac{1}{4}\arcsin\left(\frac{u}{2}\right) + C$
Parent Tip: Review the logic above to help your child master the concept of integration by substitution worksheet.
