Category: Integration

Question Number 48703 by cesar.marval.larez@gmail.com last updated on 27/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 27/Nov/18 $$3)\int {sin}^3\left(2x\right)cos\left(2x\right)dx$$$$t=sin2xdt=2cos2xdx$$$$=\frac{1}{2}\int t^{3}dt$$$$=\frac{\mathrm{1}}{\mathrm{2}}×\frac{{t}^{\mathrm{4}}…

Question Number 48643 by cesar.marval.larez@gmail.com last updated on 26/Nov/18 Commented by maxmathsup by imad last updated on 26/Nov/18 $$1)letI=\int \frac{3x+2}{(x-1)(x-2)(x^2+3)}dxletdecomposeF\left(x\right)=\frac{3x+2}{(x-1)(x-2)(x^2+3)}$$$${F}\left({x}\right)\:=\frac{{a}}{{x}−\mathrm{1}}\:+\frac{{b}}{{x}−\mathrm{2}}\:+\frac{{cx}+{d}}{{x}^{\mathrm{2}\:} +\mathrm{3}} \…

Question Number 114146 by Eric002 last updated on 17/Sep/20 $$prove$$$${\int }_0^1\frac{t^{n+2}\varphi (t,1,n+2)+ln(1-t)+t{H}_{n+1}}{t(t-1)}dt$$$$=\frac{H_{n+1}^{\left(2\right)}-{\left(H_n\right)}^2}{2}$$ Commented…

Question Number 179655 by Acem last updated on 31/Oct/22 $$Evaluate\int 6\arctan \frac{8}{w}dw$$ Answered by CElcedricjunior last updated on 05/Nov/22 $$\int 6\mathit{a}\mathit{r}\mathit{c}\mathit{t}\mathit{a}\mathit{n}\left(\frac{8}{\mathit{\omega }}\right)\mathit{d}\mathit{\omega }=\mathit{k}$$$$\boldsymbol{{posons}}\:$$\{\begin{array}{l}\mathit{u}=\mathit{a}\mathit{r}\mathit{c}\mathit{t}\mathit{a}\mathit{n}\left(\frac{8}{\mathit{\omega }}\right)\\ {\mathit{v}}^{\prime }=1\end{array}$$=>$$\{\begin{array}{l}{\mathit{u}}^{\prime }=-\frac{8}{{\mathit{\omega }}^2}\left(\frac{1}{1+{\left(\frac{8}{\mathit{\omega }}\right)}^2}\right)\\ \mathit{v}=\mathit{\omega }\end{array}$$ \…

Question Number 114102 by bemath last updated on 17/Sep/20 $$\int \frac{dx}{\tan x-\sin x}$$ Answered by bobhans last updated on 17/Sep/20 $$\int \frac{dx}{\tan x-\sin x}=-\frac{1}{2}\mathrm{cosec}{}^{2}x-\frac{1}{2}\cot x\mathrm{cosec}x$$$$+\frac{1}{2}\ln \mid \cot x+\mathrm{cosec}x\mid +c$$…