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Category: Integration

tan-x-tan-2x-tan-3x-dx-

Question Number 77447 by TawaTawa last updated on 06/Jan/20 $$\int\:\mathrm{tan}\left(\mathrm{x}\right)\:\mathrm{tan}\left(\mathrm{2x}\right)\:\mathrm{tan}\left(\mathrm{3x}\right)\:\mathrm{dx} \\ $$ Answered by peter frank last updated on 06/Jan/20 $$\mathrm{tan}\:\mathrm{3}{x}=\frac{\mathrm{tan}\:{x}+\mathrm{tan}\:\mathrm{2}{x}}{\mathrm{1}−\mathrm{tan}\:{x}\mathrm{tan}\:\mathrm{2}{x}} \\ $$$$\mathrm{tan}\:\mathrm{3}{x}−\mathrm{tan}{x}\:\mathrm{tan2}{x}\:\mathrm{tan}\:\mathrm{3}{x}=\mathrm{tan}{x}+\:\mathrm{tan}\:\mathrm{2}{x} \\ $$$$\mathrm{tan}{x}\:\mathrm{tan2}{x}\:\mathrm{tan}\:\mathrm{3}{x}=\mathrm{tan3}{x}−\:\mathrm{tan}\:\mathrm{2}{x}−\mathrm{tan}{x}\:…

Question-11868

Question Number 11868 by Nayon last updated on 03/Apr/17 Answered by sandy_suhendra last updated on 03/Apr/17 Commented by sandy_suhendra last updated on 03/Apr/17 $$\Delta\mathrm{FBA}\approx\Delta\mathrm{FB}'\mathrm{A}'\:\left(\mathrm{their}\:\mathrm{corresponding}\:\mathrm{angle}\:\:\:\:\:\right. \\…

sin-7-x-dx-

Question Number 142917 by ERA last updated on 07/Jun/21 $$\int\left(\boldsymbol{\mathrm{sin}}^{\mathrm{7}} \left(\boldsymbol{\mathrm{x}}\right)\right)\boldsymbol{\mathrm{dx}} \\ $$ Answered by Ar Brandon last updated on 07/Jun/21 $$\mathrm{2isin}\left(\mathrm{nx}\right)=\mathrm{z}^{\mathrm{n}} −\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{n}} },\:\mathrm{2isinx}=\mathrm{z}−\frac{\mathrm{1}}{\mathrm{z}} \\…

Question-142910

Question Number 142910 by BHOOPENDRA last updated on 07/Jun/21 Answered by qaz last updated on 07/Jun/21 $$\mathrm{y}\left(\mathrm{t}\right)=\mathrm{t}+\mathrm{e}^{−\mathrm{2t}} +\int_{\mathrm{0}} ^{\mathrm{t}} \mathrm{y}\left(\tau\right)\mathrm{e}^{\mathrm{2}\left(\mathrm{t}−\tau\right)} \mathrm{d}\tau \\ $$$$\mathscr{L}=\frac{\mathrm{1}}{\mathrm{s}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{s}+\mathrm{2}}+\frac{\mathscr{L}}{\mathrm{s}−\mathrm{2}}…………..\mathscr{L}=\mathscr{L}\left(\mathrm{y}\left(\mathrm{t}\right)\right)\left(\mathrm{s}\right) \\…

Question-142900

Question Number 142900 by aliibrahim1 last updated on 06/Jun/21 Commented by qaz last updated on 07/Jun/21 $$\mathrm{ln}\left(\mathrm{2sin}\:\frac{\mathrm{x}}{\mathrm{2}}\right)=−\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{cos}\:\left(\mathrm{nx}\right)}{\mathrm{n}} \\ $$ Commented by mathmax by…