Category: Integration

Question Number 97369 by  M±th+et+s last updated on 07/Jun/20 $${\int }_0^1\frac{{\left(ln\left(x\right)\right)}^2}{1+x^2}dx=\frac{{\pi }^3}{16}$$ Answered by maths mind last updated on 07/Jun/20…

Question Number 162894 by mathacek last updated on 02/Jan/22 Answered by Ar Brandon last updated on 02/Jan/22 $${\int }_0^{\frac{\pi }{2}}\ln \left(\sin x\right)dx-{\int }_0^{\frac{\pi }{2}}\ln \left(\cos x\right)dx$$$$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…

Question Number 31787 by neel1974 last updated on 14/Mar/18 $$\int \frac{4x-3}{x^2+3x+8}dx$$ Answered by sma3l2996 last updated on 14/Mar/18 $$A=\int \frac{4x-3}{x^2+3x+8}dx=2\int \frac{2x-3/2}{x^2+3x+8}dx$$$$=\mathrm{2}\int\left(\frac{\mathrm{2}{x}+\mathrm{3}}{{x}^{\mathrm{2}}…

Question Number 31747 by abdo imad last updated on 13/Mar/18 $$letgive\mid \lambda \mid <1and{u}_n={\int }_0^{\pi }\frac{cos\left(nx\right)}{1-2\lambda cosx+{\lambda }^2}$$$$provethat\sum _{n=0}^{\mathrm{\infty }}{u}_{n}isconvergentandfinditssum.$$ Commented by abdo…

Question Number 97239 by john santu last updated on 07/Jun/20 $$\int \frac{\sec {}^{3}xdx}{\sqrt{\tan x}}?$$ Commented by MJS last updated on 07/Jun/20 $$t=\sqrt{\tan x}\mathrm{leads}\mathrm{to}2\int \sqrt{t^4+1}dt\mathrm{and}\mathrm{we}\mathrm{cannot}$$$$\mathrm{solve}\:\mathrm{this}\:\mathrm{using}\:\mathrm{elementary}\:\mathrm{calculus}…