Question Number 166570 by cortano1 last updated on 22/Feb/22 Answered by bobhans last updated on 22/Feb/22 $$\:\mathrm{I}=\int\:\frac{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2}}{\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\:\mathrm{dx}\:=\:\int\frac{\mathrm{x}+\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\mathrm{dx}+\int\frac{\mathrm{2}}{\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\mathrm{dx} \\ $$$$\mathrm{I}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{d}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)}{\:\sqrt{\mathrm{x}^{\mathrm{2}}…
Question Number 101018 by Dwaipayan Shikari last updated on 29/Jun/20 $$\int_{−\infty} ^{\infty} \frac{{log}\left({sin}^{\mathrm{2}} {x}\right)}{\mathrm{1}+{x}+{e}^{{x}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 101023 by Dwaipayan Shikari last updated on 29/Jun/20 $$\int{tan}^{\frac{\mathrm{1}}{\mathrm{5}}} {x}\:{cotx}\:{secxdx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 166552 by cortano1 last updated on 22/Feb/22 $$\:\:\:\:\int_{−\infty} ^{\infty} \mathrm{cos}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\pi\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)\right)\:\mathrm{sin}\:\left(\pi\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{dx}\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 166554 by cortano1 last updated on 22/Feb/22 $$\:\:\:\int_{−\infty} ^{\infty} \mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\pi\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)\right)\:\mathrm{cos}\:\left(\pi\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 101014 by Rohit@Thakur last updated on 29/Jun/20 $${Show}\:{that} \\ $$$$\int_{−\infty} ^{+\infty} \frac{{dx}}{\mathrm{1}+\left({x}+{tanx}\right)^{\mathrm{2}} }\:\:\:=\:\:\:\pi \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 101011 by Dwaipayan Shikari last updated on 29/Jun/20 $$\int_{\mathrm{0}} ^{\infty} \frac{{sinx}}{{x}}{dx} \\ $$ Commented by Rohit@Thakur last updated on 29/Jun/20 $${Use}\:{Laplace}\:{Transform} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…
Question Number 35471 by tanmay.chaudhury50@gmail.com last updated on 19/May/18 $$\int_{{a}} ^{{b}} {f}\left({x}\right){dx}={area}\:{under}\:{the}\:{curve}\:{but}\:{say}\:{why} \\ $$$${what}\:{is}\:{the}\:{meaning}\:{of}\:\int\:\leftarrow{this}\:{sign} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 35456 by math1967 last updated on 19/May/18 $$\int\frac{{dx}}{{x}\left({x}^{\mathrm{2018}} +\mathrm{1}\right)} \\ $$ Answered by ajfour last updated on 19/May/18 $${I}=−\frac{\mathrm{1}}{\mathrm{2018}}\int\:\frac{−\mathrm{2018}{x}^{−\mathrm{19}} {dx}}{\mathrm{1}+{x}^{−\mathrm{2018}} } \\ $$$$\:\:=−\frac{\mathrm{1}}{\mathrm{2018}}\mathrm{ln}\:\mid\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2018}}…
Question Number 35440 by prof Abdo imad last updated on 19/May/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{2}{x}^{\mathrm{2}} \:\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by prof Abdo imad last updated…