不定积分也是高等数学重要的部分，对于基本的积分公式，应该做到熟记
\(\int x^{n}dx = \frac{1}{n + 1}x^{n + 1}+C\)
\(\int e^{x}dx = e^{x}+C\)
\(\int a^{x}dx=\frac{a^{x}}{\ln a}+C\)
\(\int\ln xdx = x\ln x - x + C\)
\(\int\sin xdx = -\cos x + C\)
\(\int\cos xdx=\sin x + C\)
\(\int\sec^{2}xdx=\tan x + C\)
\(\int\csc^{2}xdx=-\cot x + C\)
\(\int\sec x\tan xdx=\sec x + C\)
\(\int\csc x\cot xdx=-\csc x + C\)
\(\int\frac{1}{x}dx=\ln|x|+C\)
\(\int\frac{1}{1 + x^{2}}dx=\arctan x + C\)
\(\int\frac{1}{\sqrt{1 - x^{2}}}dx=\arcsin x + C\)
\(\int-\frac{1}{\sqrt{1 - x^{2}}}dx=\arccos x + C\)
\(\int \arcsin x\ dx = x\arcsin x + \sqrt{1 - x^{2}} + C\)
\(\int \arccos x dx = x\arccos x - \sqrt{1 - x^{2}} + C\)
\(\int \text{arccot} x\ dx = x \cdot \text{arccot} x + \frac{1}{2}\ln(1 + x^{2}) + C\)
\(\int \sin^{2}x dx = \frac{x}{2} - \frac{\sin(2x)}{4} + C\)
\(\int \cos^{2}x dx = \frac{x}{2} + \frac{\sin(2x)}{4} + C\)
\(\int \sin x \cos x dx = \frac{\sin^{2}x}{2} + C\) （也可写成\(-\frac{\cos^{2}x}{2} + C\)）
\(\int \frac{1}{(x - a)(x - b)}dx=\frac{1}{a - b}\ln\left|\frac{x - a}{x - b}\right|+C\)
\(\int \frac{x}{x^{2} + a^{2}}dx=\frac{1}{2}\ln(x^{2} + a^{2}) + C\)