[연습문제] 부정적분
1. 다음 적분 을 계산하여라. \((1)\ \displaystyle\int\sqrt{3x+1}dx={2\over9}(3x+1)^{3\over2}\) \((2)\ \displaystyle\int x(x^2-2)^2dx=\frac{(x^2-2)^3}{6}\) \((3)\ \displaystyle\int(x^2-2)^2dx=\int(x^4-2x^2+4)dx={x^5\over5}-{2\over3}x^3+4x\) \((4)\ \displaystyle\int\frac{dx}{5-2x}=-\frac{\ln|5-2x|}{2}\) \((5)\ \displaystyle\int\frac{\sqrt{x}}{1+x\sqrt{x}}dx={2\over3}\int\frac{dt}{1+t}={2\over3}\ln(1+t)={2\over3}\ln\left(1+x^{3\over2}\right)\) \((6)\ \displaystyle\int\left(1-{1\over z}\right)^2\frac{dz}{z^2}=-\int(1-t)^2dt=\frac{(1-t)^3}{3}={1\over3}\left(1-{1\over z}\right)^3\) 2. 다음 적분을 계산하여라. \((1)\ \displaystyle\int\frac{\cos3x}{\sin3x}dx={1\over3}\int\frac{d(\sin3x)}{\sin3x}=\frac{\ln|\sin3x|}{3}\) \((2)\ \displaystyle\int2\sqrt{7t-13}dt={4\over21}(7t-13)^{3/2}\) \((3)\ \displaystyle\int(\ln{x}+1)e^{x\ln{x}}dx=\int(\ln{x}+1)x^xdx=\int dt=t=x^x\) \((4)\ \displaystyle\int\frac{5x-1}{5x^2-2x+1}dx={1\over2}\int\frac{(5x^2-2x+1)'}{5x^2-2x+1}dx=\frac{\ln(5x^2-2x+1)}{2}\) \((5)\ \displaystyle\i...