Category: Integration

Question Number 59905 by Sardor2211 last updated on 15/May/19 $$\text{Missing left or extra right}$$ Commented by maxmathsup by imad last updated on 16/May/19 $${if}\:{you}\:{mean}\:{I}\:=\int\:\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{20}} {dx}\:\Rightarrow{I}\:=\int\:\sum_{{k}=\mathrm{0}} ^{\mathrm{20}}…

Question Number 59902 by Sardor2211 last updated on 15/May/19 $$\int \sin \left(x\right)dx$$ Commented by maxmathsup by imad last updated on 16/May/19 $$\int sinxdx=-cosx+C.$$ Terms…

Question Number 125421 by bemath last updated on 11/Dec/20 $$\underset{0}{\stackrel{100}{\int }}\frac{dx}{\sqrt{x(100-x)}}?$$ Answered by liberty last updated on 11/Dec/20 $${I}=\underset{\mathrm{0}} {\overset{\mathrm{100}} {\int}}\:\frac{{dx}}{\:\sqrt{{x}}\:\sqrt{\mathrm{100}−{x}}}\:;\:{let}\:\sqrt{{x}}\:=\:\mathrm{10}\:\mathrm{sin}\:{t}\: \…

Question Number 59882 by aliesam last updated on 15/May/19 $${\int }_0^{\mathrm{\infty }}\frac{sin\left(x\right)}{x(x^2+1)}dx$$ Commented by maxmathsup by imad last updated on 15/May/19 $${you}\:{are}\:{welcome}.…

Question Number 190937 by Spillover last updated on 14/Apr/23 $$\mathrm{Show}\mathrm{that}$$$$\int \frac{\mathrm{sech}\sqrt{\mathrm{x}}\tanh \sqrt{\mathrm{x}}}{\sqrt{\mathrm{x}}}=-\frac{2}{\cosh \sqrt{\mathrm{x}}}$$ Answered by ARUNG_Brandon_MBU last updated on 15/Apr/23 $$I=\int \frac{\left(\mathrm{sech}\sqrt{x}\right)\left(\tanh \sqrt{x}\right)}{\sqrt{x}}dx=\int \frac{\sinh \sqrt{x}}{\sqrt{x}{\cosh }^2\sqrt{x}}dx$$$${t}=\mathrm{cosh}\sqrt{{x}}\:\Rightarrow{dt}=\frac{\mathrm{sinh}\sqrt{{x}}}{\mathrm{2}\sqrt{{x}}}{dx}…