Category: Integration

Question Number 129975 by Algoritm last updated on 21/Jan/21 Answered by Olaf last updated on 21/Jan/21 $$\mathrm{\Omega }={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{e}^{-{\left(\frac{x}{a}\right)}^2}dx$$$$\Omega\:=\:\mathrm{2}\mid{a}\mid\int_{\mathrm{0}} ^{+\infty} {e}^{−{u}^{\mathrm{2}}…

Question Number 64419 by turbo msup by abdo last updated on 17/Jul/19 $$1)find\int \frac{dx}{x-\sqrt{1-x^2}}$$$$2)calculate{\int }_0^1\frac{dx}{x-\sqrt{1-x^2}}$$ Commented by mathmax by…

Question Number 129946 by bemath last updated on 21/Jan/21 $$\int \frac{\tan \phi +3}{\sin \phi }\mathrm{d}\phi ?$$ Answered by liberty last updated on 21/Jan/21 $$\mathrm{T}=\int (\frac{1}{\cos \phi }+\frac{3}{\sin \phi })\mathrm{d}\phi$$$$\mathrm{T}=\int (\sec \phi +3\csc \phi )\mathrm{d}\phi$$$$\:\mathrm{T}\:=\:\mathrm{ln}\:\mid\mathrm{sec}\:\varphi+\mathrm{tan}\:\varphi\mid−\mathrm{3ln}\:\mid\mathrm{cot}\:\varphi+\mathrm{csc}\:\varphi\mid\:+\:\mathrm{c} \…

Question Number 129936 by liberty last updated on 21/Jan/21 $$\mathrm{Nice}\mathrm{integral}$$$$$$$${\int }_0^{\mathrm{\infty }}\sin \left(x\right)\ln \left(x\right){\mathrm{e}}^{-x}dx$$ Answered by Lordose last updated on…

Question Number 64392 by mathmax by abdo last updated on 17/Jul/19 $$1)calculate{A}_n={\int }_0^{\mathrm{\infty }}\frac{sin\left(x^{2n}\right)}{{(x^2+1)}^2}dxwithnintegrnatural$$$$2)studytheconvergeneof\mathrm{\Sigma }{A}_n$$ Commented by mathmax…