Category: Integration

Question Number 50384 by prof Abdo imad last updated on 16/Dec/18 $$find\int \frac{dx}{(1-x^2)(1-x^3)}$$$$2)calculate{\int }_2^{\sqrt{5}}\frac{dx}{(1-x^2)(1-x^3)}$$ Commented by Abdo…

Question Number 181403 by a.lgnaoui last updated on 24/Nov/22 $$Referto\mathrm{Q}181319$$$$\int \frac{x^4+1}{x^4+x+2}dx$$$$\frac{x^4+1}{x^4+x+2}=1+\frac{x}{2(x^2+x+1)}-\frac{x}{2(x^2-x+1)}$$$$=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}}\left[\frac{\left(\mathrm{2}{x}+\mathrm{1}\right)−\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{4}}×\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)+\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)}\right. \…

Question Number 115781 by bemath last updated on 28/Sep/20 $$\underset{0}{\stackrel{\frac{1}{\sqrt{2}}}{\int }}\frac{x{\sin }^{-1}\left(x^2\right)}{\sqrt{1-x^4}}dx=?$$$$\int 2^{-x}\tanh \left(2^{1-x}\right)dx=?$$ Answered by bobhans last…

Question Number 50219 by cesar.marval.larez@gmail.com last updated on 14/Dec/18 Answered by peter frank last updated on 15/Dec/18 $$allquestionabovelieontheconcept\left(partialfraction\right)$$$$\int \frac{5\mathrm{x}+3}{{\mathrm{x}}^3-2x^2-2\mathrm{x}}=\int \frac{5\mathrm{x}+3}{x(x+1)(x-3)}$$$$\frac{\mathrm{A}}{\mathrm{x}\:}+\frac{\mathrm{B}}{\mathrm{x}−\mathrm{3}\:}+\frac{\mathrm{C}}{\mathrm{x}+\mathrm{1}} \…

Question Number 115725 by Bird last updated on 28/Sep/20 $$calculate{\int }_0^{\mathrm{\infty }}\frac{lnx}{{(x^2+x+2)}^2}dx$$ Answered by mathmax by abdo last updated on 28/Sep/20…