Category: Integration

Question Number 133360 by liberty last updated on 21/Feb/21 $$\int \sqrt{1+\sec \mathrm{x}}\mathrm{dx}?$$ Commented by som(math1967) last updated on 21/Feb/21 $$\int \sqrt{\frac{1+cosx}{cosx}}dx$$$$\sqrt{2}\int \frac{cos\frac{x}{2}}{\sqrt{1-2{sin}^2\frac{x}{2}}}dx$$$$=\frac{\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{2}}}\int\frac{{cos}\frac{{x}}{\mathrm{2}}}{\:\sqrt{\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)^{\mathrm{2}}…

Question Number 2284 by Yozzi last updated on 13/Nov/15 $$DefineacurveEbytheparametric$$$$equations$$$$x\left(t\right)={\int }_{g_1\left(t\right)}^{h_1\left(t\right)}{f}_1\left(u\right)du$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}\left({t}\right)=\int_{{g}_{\mathrm{2}} \left({t}\right)} ^{{h}_{\mathrm{2}} \left({t}\right)} {f}_{\mathrm{2}}…

Question Number 2241 by Yozzi last updated on 10/Nov/15 $$Evaluate$$$$\frac{9}{2}{\int }_0^{\pi /2}{\left(\frac{sin\theta cos\theta }{{cos}^3\theta +{sin}^3\theta }\right)}^{2}d\theta .$$ Answered by Filup last updated on…

Question Number 2212 by Yozzi last updated on 09/Nov/15 $$\int \frac{dt}{(1-kt)\sqrt{1-t^2}}=?0<k<1$$ Commented by 123456 last updated on 09/Nov/15 $$\frac{\mathrm{ln}\:\left(\sqrt{{k}^{\mathrm{2}} −\mathrm{1}}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }+{k}−{x}\right)−\mathrm{ln}\:\left(\mathrm{1}−{kx}\right)}{\:\sqrt{{k}^{\mathrm{2}} −\mathrm{1}}} \…

Question Number 2210 by Yozzi last updated on 08/Nov/15 $$Evaluate$$$${\int }_0^{\mathrm{\infty }}\frac{dx}{x^4+2x^{2}cos\alpha +1}(0<\alpha <\pi ).$$ Commented by 123456 last updated on 09/Nov/15…