1. $-\frac{1}{3} \tan(2 - 3x) + C$
2. $\frac{1}{e} \sec(2 - ex) + C$
3. $\frac{1}{2a-3} e^{2a-3} + C$ (for $a \neq \frac{3}{2}$)
4. $-\frac{1}{3} \ln|\sec(2 - 3x) + \tan(2 - 3x)| + C$
5. $\frac{1}{2} \sqrt{4x + 1} + C$
(i) $\frac{1}{2} \ln|x^2 + 1| - \tan^{-1}x + C$
(ii) $\frac{1}{2} \ln|x^2 + 1| + \tan^{-1}x + C$
(iii) $-\frac{1}{2(2x+1)} + \frac{1}{4} \ln|2x+1| + C$
(iv) $x - 2\tan^{-1}x + C$
(v) $\frac{1}{2} \ln|x^2 + 1| - \frac{1}{x^2 + 1} + C$
(vi) $\frac{1}{2(x+1)^2} - \frac{1}{x+1} + \ln|x+1| + C$
(i) $\frac{(\sin^{-1}x)^2}{2} + C$
(ii) $\frac{\sec^4x}{4} + C$
(iii) $\frac{(\log x)^5}{5} + C$
(iv) $-\frac{1}{2(x^2 + 1)} + C$
(v) $\frac{\sin^6x}{6} + C$
(i) $\frac{1}{4} \ln|1 + x^4| + C$
(ii) $\ln|e^x + e^{-x}| + C$
(iii) $x + \ln|e^x - 1| + C$
(iv) $-\frac{1}{\sqrt{x^2 + 4}} + C$
(v) $\ln|\tan x - 1| + C$
(vi) $\ln|\log(\sec x + \tan x)| + C$
Parent Tip: Review the logic above to help your child master the concept of integral worksheet with answers.
