Category: Integration

Question Number 136402 by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{find}{\mathrm{U}}_{\mathrm{n}}={\int }_{\frac{1}{\mathrm{n}}}^{\mathrm{n}}(1-\frac{1}{{\mathrm{x}}^2})\arctan (\mathrm{x}+\frac{1}{\mathrm{x}})\mathrm{dx}$$$$\mathrm{and}{\lim }_{\mathrm{n}\to \mathrm{\infty }}{\mathrm{U}}_{\mathrm{n}}$$ Terms of Service Privacy…

Question Number 136396 by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{find}{\int }_0^1\frac{{\mathrm{x}}^{\mathrm{a}}}{1-\mathrm{x}}\mathrm{dx}$$ Commented by Dwaipayan Shikari last updated on 21/Mar/21…

Question Number 136381 by mnjuly1970 last updated on 21/Mar/21 $$\dots \dots sdvancedcslculus\dots \dots$$$$ifx\in {\mathbb{R}}^{+}and::$$$$\mathit{\varphi }\left(x\right)={\int }_0^x\frac{e^t-1}{t}ln\left(\frac{x}{t}\right)dt$$$$thenprovethat::$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\Psi=\int_{\mathrm{0}} ^{\:\infty} {e}^{−{x}} \boldsymbol{\phi}\left({x}\right){dx}=\zeta\left(\mathrm{2}\right)…

Question Number 136365 by liberty last updated on 21/Mar/21 $$\int \frac{dx}{\sin x\sqrt{\cos x}}=?$$ Answered by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{I}\:=\int\:\frac{\mathrm{dx}}{\mathrm{sinx}\sqrt{\mathrm{cosx}}}\:\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{cosx}=\mathrm{t}^{\mathrm{2}} \:\Rightarrow\mathrm{x}=\mathrm{arcos}\left(\mathrm{t}^{\mathrm{2}} \right) \…

Question Number 5278 by sara last updated on 04/May/16 $$\int \{\left(3x\right)i+\left(2x\right)y\}dx=$$$$$$ Answered by FilupSmith last updated on 04/May/16 $$\int (3xi+2xy)dx$$$$=\mathrm{3}{i}\int{xdx}+\mathrm{2}{y}\int{xdx} \…