Category: Integration

Question Number 97569 by  M±th+et+s last updated on 08/Jun/20 $${\int }_0^{\frac{\pi }{4}}\sqrt{tan\left(x\right)}\sqrt{1-tan\left(x\right)}dx$$ Answered by MJS last updated on 08/Jun/20 $$\mathrm{use}\mathrm{thus}:$$$${t}=\frac{\sqrt{\mathrm{1}−\mathrm{tan}\:{x}}}{\:\sqrt{\mathrm{tan}\:{x}}}\:\rightarrow\:{dx}=−\mathrm{2cos}^{\mathrm{2}} \:{x}\sqrt{\mathrm{tan}^{\mathrm{3}}…

Question Number 32029 by abdo imad last updated on 18/Mar/18 $$calculate{\int }_0^{\mathrm{\infty }}{e}^{-\alpha x}ln\left(x\right)dxwith\alpha >0.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 97552 by bemath last updated on 08/Jun/20 $$\underset{0}{\stackrel{1}{\int }}\sqrt{\frac{x}{1-x}}\ln \left(\frac{x}{1-x}\right)dx?$$ Answered by john santu last updated on 08/Jun/20 Answered by abdomathmax…

Question Number 163072 by abdullahhhhh last updated on 03/Jan/22 $$\int \frac{\mathbf{sinx}+\mathbf{sin}3\mathbf{x}+\mathbf{sin}5\mathbf{x}+\mathbf{sin}7\mathbf{x}}{\mathbf{cosx}+\mathbf{cos}3\mathbf{x}+\mathbf{cos}5\mathbf{x}+\mathbf{cos}7\mathbf{x}}\mathbf{dx}$$ Answered by tounghoungko last updated on 03/Jan/22 $$\frac{\sin 7x+\sin x+\sin 5x+\sin 3x}{\cos 7x+\cos x+\cos 5x+\cos 3x}$$$$=\frac{2\sin 4x\cos 3x+2\sin 4x\cos x}{2\cos 4x\cos 3x+2\cos 4x\cos x}$$$$=\:\frac{\mathrm{sin}\:\mathrm{4}{x}}{\mathrm{cos}\:\mathrm{4}{x}} \…

Question Number 97526 by student work last updated on 08/Jun/20 $$\int \frac{\mathrm{dx}}{1+\sin \mathrm{x}}=?$$ Commented by bobhans last updated on 08/Jun/20 $$\frac{1}{1+\sin \mathrm{x}}\times \frac{1-\sin \mathrm{x}}{1-\sin \mathrm{x}}=\frac{1-\sin \mathrm{x}}{\cos {}^2\mathrm{x}}$$$$\int\:\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{sec}\:\mathrm{x}\:\mathrm{tan}\:\mathrm{x}\:\mathrm{dx}\:=\:\mathrm{tan}\:\mathrm{x}−\mathrm{sec}\:\mathrm{x}\:+\:\mathrm{c}…