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积分公式

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$ \int tan xdx = - ln |cos x| + C $

$ \int cot xdx=ln |sin x| + C $

$ \int sec xdx = ln |sec(x)+tg(x)|+C $

$ \int csc xdx = ln |csc(x)-ctg(x)|+ C $

$ \int \frac{dx}{a^2+ x^2}=\frac{1}{a} arctg \frac{x}{a} +C $

$ \int \frac{dx}{x^2-a^2}=\frac{1}{2a} ln|\frac{x-a}{x+ a}|+C $

$ \int \frac{dx}{a^2-x^2}= \frac{1}{2a}ln \frac{a+x}{a- x}+C $

$ \int \frac{dx}{\sqrt {a^2 - x^2}}= arcsin \frac{x}{a} + C $

$ \int \frac{dx}{cos ^2 x} = \int sec ^2 xdx = tgx + C $

$ \int \frac{dx}{sin ^2 x} = \int csc ^2 xdx = - ctgx + C $

$ \int sec x \cdot tg(x) dx = sec x + C $

$ \int csc x \cdot ctg(x) dx = - csc x + C $

$ \int a^x dx = \frac{a^x}{ln a} + C $

$ \int sh(x) dx = chx + C $

$ \int ch(x) dx = shx + C $

$ \int \frac{dx}{\sqrt {x^2 pm a^2 }} = ln (x + \sqrt {x^2 pm a^2 })+C $

$ I_n = \int_0^{\frac{\pi }{2}} sin^n(x) dx = \int_0^{\frac{\pi }{2}} cos ^n xdx = \frac{{n - 1}}{n}I_{n - 2} $

$ \int \sqrt {x^2 + a^2 } dx = \frac{x}{2}\sqrt {x^2 + a^2 } + \frac{a^2}{2}ln (x + \sqrt {x^2 + a^2 } ) + C $

$ \int \sqrt {x^2 - a^2 } dx = \frac{x}{2}\sqrt {x^2 - a^2 } - \frac{a^2}{2}ln |x + \sqrt {x^2 - a^2 }|+ C $

$ \int \sqrt {a^2 - x^2 } dx = \frac{x}{2}\sqrt {a^2 - x^2 } + \frac{a^2}{2} arcsin \frac{x}{a} + C $