Question Number 131673 by liberty last updated on 07/Feb/21 $$\:\mathrm{Nice}\:\mathrm{integral}\: \\ $$$$\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{sin}\:\left(\mathrm{ln}\:\mathrm{x}\right)}{\mathrm{ln}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by mindispower last updated on 07/Feb/21 $${ln}\left({x}\right)=−{t} \\…
Question Number 604 by 123456 last updated on 09/Feb/15 $$\underset{\mathrm{0}} {\overset{+\mathrm{1}} {\int}}\left(\underset{−\mathrm{1}} {\overset{+\mathrm{1}} {\int}}\frac{\mathrm{1}−{x}^{\mathrm{4}} {y}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{2}} {y}}{dx}\right){dy} \\ $$ Answered by prakash jain last updated…
Question Number 601 by 123456 last updated on 08/Feb/15 $$\underset{\mathrm{0}} {\overset{+\mathrm{1}} {\int}}\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{1}}{dx} \\ $$ Answered by prakash jain last updated on 08/Feb/15 $$\int_{\mathrm{0}}…
Question Number 597 by 112358 last updated on 08/Feb/15 $${Evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\mathrm{1}+{u}^{\mathrm{4}} }{du}\:{exactly}\:{if}\: \\ $$$${u}={coshx}.\: \\ $$ Commented by prakash jain last updated on 08/Feb/15…
Question Number 131674 by liberty last updated on 07/Feb/21 $$\mathrm{Given}\:\mathrm{y}=\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{satisfies}\: \\ $$$$\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\frac{\sqrt{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{y}^{\mathrm{2}} −\mathrm{1}\right)}}{\mathrm{xy}}\:=\:\mathrm{1}\: \\ $$$$\mathrm{lies}\:\mathrm{at}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{1}\right)\:\mathrm{and}\:\left(\sqrt{\mathrm{2}}\:,\mathrm{k}\right). \\ $$$$\mathrm{find}\:\mathrm{k}\:. \\ $$ Terms of Service Privacy Policy…
Question Number 571 by 123456 last updated on 30/Jan/15 $${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$$\:{if}\:{f},{g}\:{are}\:{continuos}\:{into}\:\left[{a},{b}\right]\:{and} \\ $$$${g}\:{never}\:{change}\:{sign}\:{into}\:\left[{a},{b}\right]\:{then} \\ $$$$\exists{c}\in\left[{a},{b}\right]\:{such}\:{that} \\ $$$$\underset{{a}} {\overset{{b}} {\int}}{f}\left({x}\right){g}\left({x}\right){dx}={f}\left({c}\right)\underset{{a}} {\overset{{b}} {\int}}{g}\left({x}\right){dx} \\ $$ Answered…
Question Number 570 by defgd last updated on 28/Jan/15 $$\int\:\frac{\mathrm{1}+{x}}{\left(\mathrm{2}+{x}\right)^{\mathrm{2}} }\:{e}^{{x}} \:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131637 by rs4089 last updated on 07/Feb/21 Answered by Dwaipayan Shikari last updated on 07/Feb/21 $$\int_{−\infty} ^{\infty} \frac{{sinx}}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{dx}=\int_{−\infty} ^{\infty} \frac{{sinx}}{{x}}−\frac{{xsinx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{dx}=\pi−\frac{\pi}{{e}} \\…
Question Number 66096 by sitangshu17 last updated on 09/Aug/19 $$\int\:\:\frac{\sqrt{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}}{\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:=\:? \\ $$ Commented by mathmax by abdo last updated on 09/Aug/19 $${let}\:{I}\:=\int\:\:\:\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{{x}^{\mathrm{2}}…
Question Number 131630 by Ahmed1hamouda last updated on 07/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com