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