Category: Integration

Question Number 84693 by Power last updated on 15/Mar/20 Commented by abdomathmax last updated on 15/Mar/20 $$let\phi \left(t\right)={\int }_0^{\mathrm{\infty }}\frac{sin\left(tx\right)}{x(x^2+1)}dxwehave$$$$\varphi^{'} \left({t}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({tx}\right)}{{x}^{\mathrm{2}}…

Question Number 84681 by Power last updated on 15/Mar/20 Commented by mathmax by abdo last updated on 15/Mar/20 $$I=\int \frac{15sinx+2cosx}{98sinx-7cosx}dx\Rightarrow I=\frac{15}{98}\int \frac{sinx+\frac{2}{15}cosx}{sinx-\frac{7}{98}cosx}dx$$$$letdetermineA=\int \frac{sinx+acosx}{sinx+bcosx}dxwedithechangement$$$${tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:\Rightarrow\:{A}\:=\int\frac{\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }+{a}\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}}…

Question Number 19077 by Joel577 last updated on 04/Aug/17 $$\int {\sec }^{3}xdx$$ Answered by ajfour last updated on 04/Aug/17 $$\mathrm{I}=\int \sec \theta \left(\sec {}^2\theta \mathrm{d}\theta \right)$$$$=\mathrm{sec}\:\theta\int\mathrm{sec}\:^{\mathrm{2}} \theta\mathrm{d}\theta−\int\left[\frac{\mathrm{d}}{\mathrm{d}\theta}\left(\mathrm{sec}\:\theta\right).\int\mathrm{sec}\:^{\mathrm{2}}…

Question Number 84578 by msup trace by abdo last updated on 14/Mar/20 $$calculate{\int }_0^{\frac{\pi }{4}}\frac{dx}{{(cosx+3sinx)}^2}$$ Commented by jagoll last updated on 14/Mar/20…

Question Number 84577 by msup trace by abdo last updated on 14/Mar/20 $$calculate\int \frac{dx}{cosx+cos\left(2x\right)+cos\left(3x\right)}$$ Commented by jagoll last updated on 14/Mar/20 $$\cos x+\cos 3x+\cos 2x=$$$$\mathrm{2cos}\:\mathrm{2}{x}\:\mathrm{cos}\:{x}\:+\:\mathrm{cos}\:\mathrm{2}{x}\:=\:…