Category: Integration

Question Number 90574 by niroj last updated on 24/Apr/20 $$\mathbf{Use}\mathbf{gamma}\mathbf{function}\mathbf{to}\mathbf{prove}$$$$\left(\mathrm{i}\right).{\int }_0^{\frac{\mathit{\pi }}{8}}{\mathbf{cos}}^{3}4\mathbf{x}\mathbf{dx}=\frac{1}{6}.$$$$\left(\mathbf{ii}\right).{\int }_0^{\frac{\mathit{\pi }}{6}}{\mathbf{cos}}^{4}3\mathit{\theta }{\mathbf{sin}}^{2}6\mathit{\theta }\mathbf{d}\mathit{\theta }=\frac{5\mathit{\pi }}{192}.$$ Commented by…

Question Number 90544 by jagoll last updated on 24/Apr/20 $$\int \frac{dx}{\sqrt{2-\cos x}}$$ Answered by $@ty@m123lastupdatedon24/Apr/20$$\int \frac{dx}{\sqrt{2-\frac{1-\tan {}^2\frac{x}{2}}{1+\tan {}^2\frac{x}{2}}}}$$$$\int\frac{{dx}}{\:\sqrt{\frac{\mathrm{2}+\mathrm{2tan}\:^{\mathrm{2}} \frac{{x}}{\mathrm{2}}+\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}}…

Question Number 90508 by frc2crc last updated on 24/Apr/20 $$\underset{n=1}{\sum ^{\mathrm{\infty }}}\left(\frac{1}{n^m{(1+n)}^m}\right)$$$$whatisthegeneralforthissum$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 90480 by M±th+et£s last updated on 23/Apr/20 $$\int e^x\frac{(1+cos\left(x\right))(1-sin\left(x\right))}{{(e^{x}cos\left(x\right)+1)}^2}dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 156009 by zainaltanjung last updated on 07/Oct/21 $$\mathrm{Please}\mathrm{calculate}$$$$1).\int \sin {}^5\mathrm{x}\mathrm{dx}$$$$2).\int \cos {}^2\mathrm{x}\mathrm{dx}$$$$3).\int \tan {}^3\mathrm{x}.\sec {}^5\mathrm{x}\mathrm{dx}$$$$4).\int \cos 5\mathrm{x}.\cos 3\mathrm{x}\mathrm{dx}$$$$\left.\mathrm{5}\right).\:\int\:\:\frac{\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}}{\mathrm{sec}\:^{\mathrm{2}}…