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Category: Integration

ln-2-xsin-x-dx-

Question Number 65704 by mmkkmm000m last updated on 03/Aug/19 $$\int{ln}^{\mathrm{2}} {xsin}\left({x}\right){dx} \\ $$ Commented by Tinku Tara last updated on 02/Aug/19 $$\mathrm{Can}\:\mathrm{please}\:\mathrm{use}\:\mathrm{smaller}\:\mathrm{font}\:\mathrm{size} \\ $$ Terms…

evaluate-f-a-b-a-b-b-x-x-a-dx-

Question Number 164 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate}\:{f}\left({a},{b}\right)=\underset{{a}} {\overset{{b}} {\int}}\left({b}−{x}\right)\left({x}−{a}\right){dx} \\ $$ Answered by prakash jain last updated on 14/Dec/14 $$\left({b}−{x}\right)\left({x}−{a}\right)=−{x}^{\mathrm{2}} +\left({a}+{b}\right){x}−{ab} \\…

real-analysis-prove-0-1-ln-ln-1-x-ln-2-x-dx-3-2-

Question Number 131227 by mnjuly1970 last updated on 02/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{real}\:\:{analysis}\:… \\ $$$$\:\:\:\:\:\:{prove}:: \\ $$$$\:\:\:\boldsymbol{\Omega}=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left({ln}\left(\frac{\mathrm{1}}{{x}}\right)\right){ln}^{\mathrm{2}} \left({x}\right){dx}=\mathrm{3}−\mathrm{2}\gamma \\ $$$$ \\ $$ Answered by Dwaipayan Shikari…

evaluate-0-1-sin-x-x-ln-x-dx-

Question Number 151 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{\mathrm{sin}\:{x}}{{x}}\mathrm{ln}\:{x}\:{dx} \\ $$ Answered by prakash jain last updated on 13/Dec/14 $$\mathrm{sin}\:{x}={x}−\frac{{x}^{\mathrm{3}} }{\mathrm{3}!}+\frac{{x}^{\mathrm{5}} }{\mathrm{5}!}−\frac{{x}^{\mathrm{7}}…

0-1-r-1-n-x-r-k-1-n-1-x-k-dx-

Question Number 65681 by aliesam last updated on 01/Aug/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\underset{{r}=\mathrm{1}} {\overset{{n}} {\prod}}\left({x}+{r}\right)\right)\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{{x}+{k}}\right)\:{dx} \\ $$ Answered by Tanmay chaudhury last updated on…

let-A-n-cos-2-n-x-x-2-3-2-dx-1-calculate-A-n-interms-of-n-2-find-nsture-of-the-serie-A-n-and-n-n-A-n-

Question Number 65679 by mathmax by abdo last updated on 01/Aug/19 $${let}\:\:{A}_{{n}} =\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left(\mathrm{2}^{{n}} {x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right){find}\:{nsture}\:{of}\:{the}\:{serie}\:\Sigma{A}_{{n}} \:\:\:\:{and}\:\Sigma{n}^{{n}} \:{A}_{{n}}…