Category: Integration

Question Number 118419 by bramlexs22 last updated on 17/Oct/20 $$\int \frac{2\sin 2x}{4\cos x+\sin 2x}dx$$ Commented by bramlexs22 last updated on 17/Oct/20 $$yes\dots thankyouallmaster$$ Answered by peter…

Question Number 118347 by bramlexs22 last updated on 17/Oct/20 $$\int \frac{dx}{\sqrt{x}+\sqrt[3]{x}}$$ Answered by benjo_mathlover last updated on 17/Oct/20 $$settingx=r^6$$$$\int\:\frac{\mathrm{6}{r}^{\mathrm{5}} }{{r}^{\mathrm{3}} +{r}^{\mathrm{2}} }\:{dr}\:=\:\:\int\frac{\mathrm{6}{r}^{\mathrm{3}}…

Question Number 118338 by benjo_mathlover last updated on 17/Oct/20 $$solve\int \frac{dx}{3-5\sin x}$$ Answered by Dwaipayan Shikari last updated on 17/Oct/20 $$\int \frac{dx}{3-5sinx}$$$$=\mathrm{2}\int\frac{{dt}}{\mathrm{3}−\frac{\mathrm{10}{t}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}}.\frac{\mathrm{1}}{\mathrm{1}+{t}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\:{t}={tan}\frac{{x}}{\mathrm{2}}…

Question Number 183865 by Michaelfaraday last updated on 31/Dec/22 Answered by MJS_new last updated on 31/Dec/22 $$=\underset{0}{\stackrel{\pi }{\int }}\mid 1-2\sin \frac{x}{2}\mid dx=$$$$=\underset{\mathrm{0}} {\overset{\pi/\mathrm{3}} {\int}}\left(\mathrm{2sin}\:\frac{{x}}{\mathrm{2}}\:−\mathrm{1}\right){dx}+\underset{\pi/\mathrm{3}} {\overset{\pi} {\int}}\left(\mathrm{1}−\mathrm{2sin}\:\frac{{x}}{\mathrm{2}}\right){dx}=…

Question Number 183844 by Michaelfaraday last updated on 30/Dec/22 Answered by MJS_new last updated on 31/Dec/22 $$\int \frac{dx}{\sqrt{2x-1}+\sqrt{x-3}}=$$$$=\int \frac{\sqrt{2x-1}-\sqrt{x-3}}{(\sqrt{2x-1}+\sqrt{x-3})\left(\sqrt{2x-1-}\sqrt{x-3}\right)}dx=$$$$=\int \frac{\sqrt{2x-1}}{x+2}dx-\int \frac{\sqrt{x-3}}{x+2}dx=$$$$\mathrm{with}u=\sqrt{2x-1}\mathrm{and}v=\sqrt{x-3}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{easy}\mathrm{to}\mathrm{get}$$$$=\mathrm{2}\sqrt{\mathrm{2}{x}−\mathrm{1}}−\mathrm{2}\sqrt{\mathrm{5}}\mathrm{arctan}\:\frac{\sqrt{\mathrm{2}{x}−\mathrm{1}}}{\:\sqrt{\mathrm{5}}}\:−\mathrm{2}\sqrt{{x}−\mathrm{3}}+\mathrm{2}\sqrt{\mathrm{5}}\mathrm{arctan}\:\frac{\sqrt{{x}−\mathrm{3}}}{\:\sqrt{\mathrm{5}}}\:+{C}…