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Category: Integration

0-2pi-dx-2-cos-x-

Question Number 85568 by jagoll last updated on 23/Mar/20 $$\int\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\:}}\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{2}}−\mathrm{cos}\:\mathrm{x}} \\ $$ Commented by jagoll last updated on 23/Mar/20 $$\mathrm{I}\:=\:\int\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\:}}\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{2}}−\mathrm{cos}\:\mathrm{x}} \\…

Calculate-0-x-x-4-14x-2-1-5-4-dx-2-3-4-4-2pi-

Question Number 151068 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}\:\:::\:\int_{\mathrm{0}} ^{\infty} \frac{\sqrt{\mathrm{x}}}{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{14x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{5}}{\mathrm{4}}} }\mathrm{dx}=\frac{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right)}{\mathrm{4}\sqrt{\mathrm{2}\pi}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Calculate-x-x-a-sin-pix-dx-2-a-1-a-pi-a-gt-0-

Question Number 151065 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}\:\:\:::\:\:\int_{−\infty} ^{+\infty} \frac{\Gamma\left(\mathrm{x}\right)}{\Gamma\left(\mathrm{x}+\mathrm{a}\right)}\mathrm{sin}\:\left(\pi\mathrm{x}\right)\mathrm{dx}=\frac{\mathrm{2}^{\mathrm{a}−\mathrm{1}} }{\Gamma\left(\mathrm{a}\right)}\pi\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{a}>\mathrm{0}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Calculate-0-pi-sin-x-2-arctan-2-sin-x-1-dx-2-ln-1-2-1-1-2-pi-

Question Number 151067 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}\:\:::\:\:\int_{\mathrm{0}} ^{\pi} \mathrm{sin}\:\frac{\mathrm{x}}{\mathrm{2}}\centerdot\mathrm{arctan}\left(\frac{\mathrm{2}}{\mathrm{sin}\:\mathrm{x}}−\mathrm{1}\right)\mathrm{dx}=\sqrt{\mathrm{2}}\mathrm{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)+\left(\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)\pi \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Calculate-0-pi-arctan-2sin-2-x-1-2-2-cos-x-2-2-dx-piarctan-5-1-2-

Question Number 151064 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}\:\:::\:\:\int_{\mathrm{0}} ^{\pi} \mathrm{arctan}\left(\frac{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{1}−\mathrm{2}\sqrt{\mathrm{2}}\varphi\mathrm{cos}\:\mathrm{x}+\mathrm{2}\varphi^{\mathrm{2}} }\right)\mathrm{dx}=\pi\mathrm{arctan}\:\sqrt{\varphi}\:\:\:\:\:\:\:\:\:\:\left(\varphi=\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Calculate-0-pi-2-x-cot-x-ln-2-cos-xdx-pi-3-24-ln2-pi-6-ln-3-2-3-16-pi-3-

Question Number 151061 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}\:\:::\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{x}\centerdot\mathrm{cot}\:\mathrm{x}\centerdot\mathrm{ln}^{\mathrm{2}} \mathrm{cos}\:\mathrm{xdx}=\frac{\pi^{\mathrm{3}} }{\mathrm{24}}\mathrm{ln2}+\frac{\pi}{\mathrm{6}}\mathrm{ln}^{\mathrm{3}} \mathrm{2}−\frac{\mathrm{3}}{\mathrm{16}}\pi\zeta\left(\mathrm{3}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com