Category: Integration

Question Number 137501 by mnjuly1970 last updated on 03/Apr/21 $$\dots .advanced\dots .calculus\dots .$$$$provethat::$$$$\mathit{\varphi }={\int }_0^1\frac{ln\left(x\right).ln(1-x)}{1+x}dx=\frac{13}{8}\zeta \left(3\right)-\frac{{\pi }^2}{4}ln\left(2\right)\dots .$$ Answered by Ñï= last updated on…

Question Number 137461 by mathlove last updated on 03/Apr/21 Answered by Ñï= last updated on 03/Apr/21 $$\int \frac{1+x^2}{2x+x^3}dx=\frac{1}{3}\int \frac{2+3x^2+1}{2x+x^3}dx=\frac{1}{3}ln\mid 2x+x^3\mid +\frac{1}{3}\int \frac{dx}{x(2+x^2)}$$$$=\frac{\mathrm{1}}{\mathrm{3}}{ln}\mid\mathrm{2}{x}+{x}^{\mathrm{3}}…

Question Number 6390 by FilupSmith last updated on 25/Jun/16 $$\mathrm{Solve}:$$$$I\left(n\right)={\int }_0^n{(-1)}^{\lfloor x\rfloor }{x}^{2}dx$$ Commented by prakash jain last updated on…

Question Number 137448 by liberty last updated on 03/Apr/21 $${\int }_0^{3/4}\frac{dx}{(x+1)\sqrt{x^2+1}}?$$ Answered by MJS_new last updated on 03/Apr/21 $$\int\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}= \…

Question Number 137439 by mnjuly1970 last updated on 02/Apr/21 $$\dots \dots nicecalculus\dots ..$$$$provethat::$$$$\mathit{\chi }={\int }_0^1\frac{ln(x+\sqrt{1-x^2})}{x}dx=\frac{{\pi }^2}{16}\dots .$$ Answered by mindispower last updated…