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基本积分表
∫ x a d x = 1 a + 1 x a + 1 + C ( a ∈ R , a ≠ − 1 ) ∫x^a\mathrm{d}x\ =\frac{1}{a+1}x^{a+1}+C(a∈R,a≠−1) ∫xadx =a+11xa+1+C(a∈R,a=−1) ∫ 1 x d x = l n ∣ x ∣ + C ∫\frac{1}{x} \mathrm{d}x\ =ln|x|+C ∫x1dx =ln∣x∣+C ∫ c o s x d x = s i n x + C ∫cosx\mathrm{d}x\ =sinx+C ∫cosxdx =sinx+C ∫ s i n x d x = − c o s x + C ∫sinx\mathrm{d}x\ =−cosx+C ∫sinxdx =−cosx+C ∫ t a n x d x = − l n ∣ c o s x ∣ + C ∫tanx\mathrm{d}x\ =−ln|cosx|+C ∫tanxdx =−ln∣cosx∣+C ∫ c o t x d x = l n ∣ s i n x ∣ + C ∫cotx\mathrm{d}x\ =ln|sinx|+C ∫cotxdx =ln∣sinx∣+C ∫ 1 c o s 2 x d x = t a n x + C ∫\frac{1}{cos^2x}\mathrm{d}x\ =tanx+C ∫cos2x1dx =tanx+C ∫ 1 1 + x 2 d x = a r c t a n x + C ∫\frac{1}{1+x^2}\mathrm{d}x\ =arctanx+C ∫1+x21dx =arctanx+C ∫ e x d x = e x + C ∫e^x\mathrm{d}x\ =e^x+C ∫exdx =ex+C ∫ x e x d x = e x ( x − 1 ) + C ∫xe^x\mathrm{d}x\ =e^x(x−1)+C ∫xexdx =ex(x−1)+C ∫ a x d x = 1 l n a a x + C ∫a^x\mathrm{d}x\ =\frac{1}{lna}ax+C ∫axdx =lna1ax+C
常用积分表
∫ s i n 2 x d x = 12 ( x − s i n x c o s x ) + C ∫sin^2x\mathrm{d}x\ =12(x−sinxcosx)+C ∫sin2xdx =12(x−sinxcosx)+C ∫ c o s 2 x d x = 12 ( x + s i n x c o s x ) + C ∫cos^2x\mathrm{d}x\ =12(x+sinxcosx)+C ∫cos2xdx =12(x+sinxcosx)+C ∫ s e c x d x = l n ∣ t a n x + s e c x ∣ + C ∫secx\mathrm{d}x\ =ln|tanx+secx|+C ∫secxdx =ln∣tanx+secx∣+C ∫ l n x d x = x l n x − x + C ∫lnx\mathrm{d}x\ =xlnx−x+C ∫lnxdx =xlnx−x+C ∫ a 2 − x 2 d x = 1 2 ( x a 2 − x 2 + a 2 a r c s i n x a ) + C ∫\sqrt{a^2−x^2}\mathrm{d}x\ =\frac{1}{2}(x\sqrt{a^2−x^2}+a^2arcsin{\frac{x}{a}})+C ∫a2−x2dx =21(xa2−x2+a2arcsinax)+C ∫ 1 1 − x 2 d x = a r c s i n ( x ) + C ∫\frac{1}{\sqrt{1−x^2}}\mathrm{d}x\ =arcsin(x)+C ∫1−x21dx =arcsin(x)+C ∫ 1 1 + x 2 d x = l n ( x + 1 + x 2 ) + C = s i n − 1 h . x + C ∫\frac{1}{\sqrt{1+x^2}}\mathrm{d}x\ =ln(x+\sqrt{1+x^2)}+C=sin^{-1}h.{x}+C ∫1+x21dx =ln(x+1+x2)+C=sin−1h.x+C
- 最后检查于2021/10/26,15:21
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