Научно-исследовательский сайт Вячеслава Горчилина
Все формулы
Формулы. Математика
Некоторые неберущиеся интегралы
$\int e^{\pm x^2} dx$
$\int \sin x^2 dx$
$\int \cos x^2 dx$
$\int {\sin x \over x} dx$
$\int {\cos x \over x} dx$
$\int {dx \over \ln x}$
$\int {e^x \over x} dx$
$\int {e^x \over x^n} dx$
$\int {\sin x \over x^n} dx$
$\int {\cos x \over x^n} dx$
$\int {dx \over \sqrt{(1-x^2)(1-k^2x^2)}}$
$\int {x^2 dx \over \sqrt{(1-x^2)(1-k^2x^2)}}$
$\int {dx \over \sqrt{1-k^2 \sin^2 x}}$
$\int \sqrt{1-k^2 \sin^2 x}\,dx$
$\int {xdx \over \sin x}$
$\int {x^2 dx \over \sin x}$
$\int {xdx \over \sin^3 x}$
$\int {\sin^2 x \over x} dx$
$\int {\cos^2 x \over x} dx$
$\int {xdx \over \cos x}$
$\int {xdx \over \cos^3 x}$
$\int x\,\mathtt{tg}\,x\,dx$
$\int {\mathtt{tg}\,x \over x} dx$
$\int x\,\mathtt{ctg}\,x\,dx$
$\int {\mathtt{ctg}\,x \over x} dx$
$\int {\mathtt{arcsin}\,x \over x} dx$
$\int {\mathtt{arccos}\,x \over x} dx$
$\int {\mathtt{arctg}\,x \over x} dx$
$\int {\mathtt{arcctg}\,x \over x} dx$
$\int {e^x \over x^2} dx$
$\int {xdx \over \ln x}$
$\int {x^2 dx \over \ln x}$
$\int {dx \over x^2\ln x}$
$\int {\ln(ax+b) \over x} dx$
$\int {\ln(x+\sqrt{x^2+1}) \over x} dx$
$\int \ln \sin x\,dx$
$\int \ln \cos x\,dx$
$\int \ln \mathtt{tg}\,x\,dx$
$\int e^x \ln x \, dx$
$\int {\mathtt{sh}\,x \over x} dx$
$\int {\mathtt{ch}\,x \over x} dx$
$\int {\mathtt{sh}\,x \over x^2} dx$
$\int {\mathtt{sh}^2\,x \over x} dx$
$\int {x dx \over \mathtt{sh}\,x}$
$\int {\mathtt{ch}^2\,x \over x} dx$
$\int {x dx \over \mathtt{ch}\,x}$
$\int e^{\pm x^2} dx$
$\int \sin x^2 dx$
$\int \cos x^2 dx$
$\int {\sin x \over x} dx$
$\int {\cos x \over x} dx$
$\int {dx \over \ln x}$
$\int {e^x \over x} dx$
$\int {e^x \over x^n} dx, \quad n \in N$
$\int {\sin x \over x^n} dx, \quad n \in N$
$\int {\cos x \over x^n} dx, \quad n \in N$
$\int {dx \over \sqrt{(1-x^2)(1-k^2x^2)}}, \quad 0 \lt k \lt 1$
$\int {x^2 dx \over \sqrt{(1-x^2)(1-k^2x^2)}}, \quad 0 \lt k \lt 1$
$\int {dx \over \sqrt{1-k^2 \sin^2 x}}, \quad 0 \lt k \lt 1$
$\int \sqrt{1-k^2 \sin^2 x}\,dx, \quad 0 \lt k \lt 1$
$\int {xdx \over \sin x}$
$\int {x^2 dx \over \sin x}$
$\int {xdx \over \sin^3 x}$
$\int {\sin^2 x \over x} dx$
$\int {\cos^2 x \over x} dx$
$\int {xdx \over \cos x}$
$\int {xdx \over \cos^3 x}$
$\int x\,\mathtt{tg}\,x\,dx$
$\int {\mathtt{tg}\,x \over x} dx$
$\int x\,\mathtt{ctg}\,x\,dx$
$\int {\mathtt{ctg}\,x \over x} dx$
$\int {\mathtt{arcsin}\,x \over x} dx$
$\int {\mathtt{arccos}\,x \over x} dx$
$\int {\mathtt{arctg}\,x \over x} dx$
$\int {\mathtt{arcctg}\,x \over x} dx$
$\int {e^x \over x^2} dx$
$\int {xdx \over \ln x}$
$\int {x^2 dx \over \ln x}$
$\int {dx \over x^2\ln x}$
$\int {\ln(ax+b) \over x} dx, \quad a \neq 0$
$\int {\ln(x+\sqrt{x^2+1}) \over x} dx$
$\int \ln \sin x\,dx$
$\int \ln \cos x\,dx$
$\int \ln \mathtt{tg}\,x\,dx$
$\int e^x \ln x \, dx$
$\int {\mathtt{sh}\,x \over x} dx$
$\int {\mathtt{ch}\,x \over x} dx$
$\int {\mathtt{sh}\,x \over x^2} dx$
$\int {\mathtt{sh}^2\,x \over x} dx$
$\int {x dx \over \mathtt{sh}\,x}$
$\int {\mathtt{ch}^2\,x \over x} dx$
$\int {x dx \over \mathtt{ch}\,x}$