Category: Integration

Question Number 68141 by MJS last updated on 06/Sep/19 $$\mathrm{the}2\mathrm{formulas}\mathrm{for}\mathrm{solving}\int \frac{dx}{x^3+px+q}\mathrm{with}$$$$“{\mathrm{nasty}}^{″}\mathrm{solutions}\mathrm{of}{x}^3+px+q=0\mathrm{with}p,q\in \mathbb{R}$$$$$$$$\mathrm{case}1$$$$D=\frac{p^3}{27}+\frac{q^2}{4}>0\Rightarrow x^3+px+q=0\mathrm{has}\mathrm{got}1\mathrm{real}$$$$\mathrm{and}\:\mathrm{2}\:\mathrm{conjugated}\:\mathrm{complex}\:\mathrm{solutions}…

Question Number 68116 by aliesam last updated on 05/Sep/19 $$\int \frac{dx}{sin2x-sec\left(x\right)}$$ Commented by MJS last updated on 06/Sep/19 $$\mathrm{look}\mathrm{at}\mathrm{question}68141$$ Answered by MJS…

Question Number 68094 by mhmd last updated on 04/Sep/19 $$\int dx/\sqrt[x]{{(\pi +e)}^{x^2}}$$ Answered by MJS last updated on 05/Sep/19 $$\int\frac{{dx}}{\:\sqrt[{{x}}]{\left(\pi+\mathrm{e}\right)^{{x}^{\mathrm{2}} } }}=\int\frac{{dx}}{\left(\pi+\mathrm{e}\right)^{{x}} }=−\frac{\mathrm{1}}{\left(\pi+\mathrm{e}\right)^{{x}}…

Question Number 2526 by Filup last updated on 22/Nov/15 $$\mathrm{Evaluate}:\underset{-\mathrm{\infty }}{\stackrel{\mathrm{\infty }}{\int }}{e}^{-x^2}dx$$$$\mathrm{Please}\mathrm{show}\mathrm{and}\mathrm{explain}\mathrm{working}$$ Commented by Filup last updated on 22/Nov/15…

Question Number 68046 by mhmd last updated on 03/Sep/19 Answered by mind is power last updated on 03/Sep/19 $$\frac{d\left(e^{\frac{sin\left(2x\right)}{2}}\right)}{dx}=cos\left(2x\right)e^{sin\left(x\right)cos\left(x\right)}$$$$\int\frac{{e}^{{sin}\left({x}\right){cos}\left({x}\right)} {cos}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{e}^{{sin}\left(\mathrm{2}{x}\right)} }{dx} \…