Category: Integration

Question Number 179175 by Acem last updated on 26/Oct/22 $$Find\int x^5\sqrt{x^3+1}dx$$$$$$$$Answer:I=\frac{2}{45}(3x^3-2)\sqrt{{(x^3+1)}^3}+c$$$$$$ Commented by…

Question Number 113630 by mathmax by abdo last updated on 14/Sep/20 $$\mathrm{explicit}\mathrm{g}\left(\mathrm{a}\right)={\int }_0^{\frac{\pi }{4}}\ln (1+{\mathrm{acos}}^2\theta )\mathrm{d}\theta$$ Answered by Dwaipayan Shikari last updated on 15/Sep/20…

Question Number 113628 by mathmax by abdo last updated on 14/Sep/20 $$\mathrm{find}\int \frac{\mathrm{dx}}{(\mathrm{x}+1)\sqrt{{\mathrm{x}}^2-1}+(\mathrm{x}-1)\sqrt{{\mathrm{x}}^2+1}}$$ Answered by MJS_new last updated on 16/Sep/20 $$\int\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}+\left({x}−\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}}…

Question Number 48078 by cesar.marval.larez@gmail.com last updated on 19/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 19/Nov/18 $$21)\int e^{2-x}dx$$$$t=2-xdt=-dx$$$$\int e^t\times -dt$$$$=\left(−\mathrm{1}\right){e}^{{t}}…

Question Number 113600 by eric last updated on 14/Sep/20 $$Prouverque$$$$\beta (a,b)=\frac{\mathrm{\Gamma }\left(a\right)\mathrm{\Gamma }\left(b\right)}{\mathrm{\Gamma }(a+b)}={\int }_0^1{x}^{a-1}{(1-x)}^{b-1}dx$$ Answered by Dwaipayan Shikari last updated on…