a) $\frac{2}{3}(5+2x)^{3/2} + C$
b) $\frac{1}{36}(3x^2 - 4)^6 + C$
c) $\frac{1}{3}\ln^3 x + C$
d) $\frac{3}{\sqrt{5-2x}} + C$
e) $\sin\left(\frac{1}{x}\right) + C$
f) $-\frac{5}{2}(1-6x)^{2/3} + C$
g) $-\frac{2}{3}\cos\left(\frac{3x-5}{2}\right) + C$
h) $-\frac{2}{9}(6-x^3)^{2/3} + C$
i) $-3\cot\left(\frac{x-2}{3}\right) + C$
j) $\frac{1}{2}\ln(x^2 + 1) + C$
k) $\frac{3}{4}(x^4 + 4)^{2/3} + C$
l) $\frac{1}{5}\ln|\sin(5x+9)| + C$
m) $\frac{1}{\ln 4}\cdot\frac{2^x}{1+4^x} + C$ (Note: This integral does not have an elementary antiderivative. The provided answer is incorrect. The correct approach involves substitution and results in a non-elementary function.)
n) $-e^{1/x} + C$
o) $\frac{2}{3}(1+\ln x)^{3/2} + C$
p) $2\sqrt{x} - 2\arctan(\sqrt{x}) + C$
q) $\frac{2}{3}\arctan\left(\frac{x}{3}\right) + C$
r) $-\frac{1}{6(5+3x)^2} + C$
s) $-\frac{1}{3}\sqrt{1-x^6} + C$
t) $-\frac{1}{2}e^{\cos^2 x} + C$
u) $\frac{3}{2}\sqrt{\ln 3x} + C$
v) $\frac{3}{2}\sqrt[3]{\sin^2 x} + C$
w) $-\frac{1}{7}\cos 7x + C$
x) $-\frac{3}{5}e^{-x^5 + 2} + C$
y) $\int x^2 e^{x^3} dx = \frac{1}{3}e^{x^3} + C$
z) $-\frac{1}{4(x^2 - 4)^2} + C$
Z) $-\frac{1}{2}\cos\left(\frac{1}{x^2}\right) + C$
Parent Tip: Review the logic above to help your child master the concept of indefinite integral worksheet.
