Category: Integration

Question Number 129318 by mnjuly1970 last updated on 14/Jan/21 $$\dots laplacetransformation..$$$$\mathcal{L}({te}^{-t}\lfloor t\rfloor )=?$$$$note:\lfloor x\rfloor isfloorof{}^{″}x{}^{″}\dots$$$$\dots \dots \dots \dots ..$$$$$$ Answered by mathmax by…

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Question Number 129274 by bramlexs22 last updated on 14/Jan/21 $$\int \frac{\cos {}^2\mathrm{x}+\cos \mathrm{x}}{1+\sin \mathrm{x}+\cos \mathrm{x}}\mathrm{dx}?$$ Answered by liberty last updated on 14/Jan/21 $$\int \frac{\cos \mathrm{x}(\cos \mathrm{x}+1)}{\sin \mathrm{x}+2\cos {}^2\left(\frac{\mathrm{x}}{2}\right)}\mathrm{dx}=\int \frac{\cos \mathrm{x}\left(2\cos {}^2\left(\frac{\mathrm{x}}{2}\right)\right)}{2\cos \left(\frac{\mathrm{x}}{2}\right)[\sin \left(\frac{\mathrm{x}}{2}\right)+\cos \left(\frac{\mathrm{x}}{2}\right)]}\mathrm{dx}=$$$$\:\int\:\frac{\mathrm{cos}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\left(\mathrm{cos}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)+\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\right)\left(\mathrm{cos}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)−\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\right)}{\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)}\mathrm{dx}=…

Question Number 129275 by abdurehime last updated on 14/Jan/21 $$\int {\mathrm{e}}^{{\mathrm{x}}^{\mathrm{x}}}\mathrm{dx}??????$$ Commented by abdurehime last updated on 14/Jan/21 $$\mathrm{no}\mathrm{one}????$$ Commented…

Question Number 129269 by bramlexs22 last updated on 14/Jan/21 $${\int }_1^a\frac{4\sqrt{x}+k}{\sqrt{x}+1}=4a+3.\mathrm{Find}\mathrm{the}\mathrm{value}$$$$\mathrm{of}{\int }_1^a\frac{1}{\sqrt{x}+1}dx.$$ Answered by liberty last updated on 14/Jan/21…