Final Answer:
(1) $\frac{1}{3}\ln|x| - \frac{1}{6}\ln|x^2+3| + \frac{1}{\sqrt{3}}\tan^{-1}\left(\frac{x}{\sqrt{3}}\right) + C$
(2) $3x - 2\ln|x-3| + 3\ln|x+1| + C$
(3) $\ln|x-1| + \frac{3}{x-1} + C$
(4) $\frac{1}{2}\ln\left|\frac{x-2}{x+2}\right| + \frac{1}{2}\tan^{-1}(2x) + C$
(5) $\ln|x+1| - \frac{1}{x+1} + C$
(6) $\ln|x-1| - \ln|x^2+x+1| + C$
(7) $2x + \ln|x-1| + C$
(8) $\ln|x+3| + 2\ln|x+4| + C$
(9) $\frac{1}{4}\ln\left|\frac{x-2}{x+2}\right| + C$
(10) $\ln|x+3| - \ln|x-3| + C$
(11) $2\ln|x| - \ln|x+5| + C$
(12) $\frac{1}{8}\ln\left|\frac{x-4}{x+4}\right| + C$
(13) $x + \ln|x+1| + C$
(14) $\ln|x| - \frac{1}{2}\ln|x^2-1| + C$
(15) $-\frac{1}{2x} + \frac{1}{4}\ln\left|\frac{x}{x+2}\right| + C$
(16) $\ln|x| - \ln|x^2+2| + C$
(17) $\ln|x-3| + \frac{3}{x-3} + C$
(18) $\frac{3}{2}\ln|x-3| + \frac{1}{2}\ln|x+2| + C$
Parent Tip: Review the logic above to help your child master the concept of calculus 2 worksheet.
