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Question Number 212886 by MrGaster last updated on 26/Oct/24 $$\int \frac{\sin 10x}{\sin x}dx.$$ Answered by Ghisom last updated on 26/Oct/24 $$\int \frac{\sin 10x}{\sin x}dx=$$$$=4\int \cos x(\cos 8x+\cos 4x+\frac{1}{2})dx=$$$$\:\:\:\:\:\left[{t}=\mathrm{sin}\:{x}\right] \…

Question Number 212906 by issac last updated on 26/Oct/24 $$\mathrm{Pls}\mathrm{i}\mathrm{need}\mathrm{a}\mathrm{help}..$$$$\mathrm{from}\mathrm{Ordinary}\mathrm{differantial}\mathrm{Equation}$$$$t^2{y}^{\left(2\right)}\left(t\right)+t\cdot y^{\left(1\right)}\left(t\right)+(t^2-{\nu }^2)y\left(t\right)=0$$$$\mathrm{we}\mathrm{Already}\mathrm{Know}$$$$\mathrm{Solution}\:{y}\left({t}\right)={C}_{\mathrm{1}} {J}_{\nu} \left({t}\right)+{C}_{\mathrm{2}}…

Question Number 212798 by MrGaster last updated on 24/Oct/24 $$\underset{x\to \mathrm{\infty }}{\lim }{(1+\frac{1}{x})}^{\frac{x^2}{e^x}}=?$$ Answered by mehdee7396 last updated on 24/Oct/24 $${lim}_{{x}\rightarrow\infty} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)=\mathrm{1}\:\:\:\:\&\:\:\:\:{lim}_{{x}\rightarrow\infty}…

Question Number 212816 by Akayx last updated on 24/Oct/24 Answered by mahdipoor last updated on 24/Oct/24 $$f\left(t\right)=\underset{k=0}{\sum ^{\mathrm{\infty }}}2(t-4k)(u_{4k}-u_{4k+2})=$$$$\mathrm{2}\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\left[\left({t}−\mathrm{4}{k}\right){u}_{\mathrm{4}{k}}…

Question Number 212765 by issac last updated on 23/Oct/24 $$\mathrm{i}\mathrm{generalized}\mathbf{Bessel}{\mathbf{function}}^{\prime }\mathrm{s}$$$$\mathrm{Laplace}\mathrm{Transform}$$$$\mathrm{L}.\mathrm{T}{J}_{\nu }\left(z\right)=\frac{{(s+\sqrt{s^2+1})}^{-\nu }}{\sqrt{s^2+1}},s\in [0,\mathrm{\infty }),\nu \in \mathbb{R}$$$$\mathrm{L}.\mathrm{T}\:{Y}_{\nu} \left({z}\right)=\frac{\mathrm{cot}\left(\pi\nu\right)\left({s}+\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}\right)^{−\nu} }{\:\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}}−\frac{\mathrm{csc}\left(\pi\nu\right)\left({s}+\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}\right)^{\nu}…