Category: Integration

Question Number 11149 by suci last updated on 14/Mar/17 $$\int x^5\sqrt[3]{x^3+1}dx=\dots ???$$ Answered by ajfour last updated on 14/Mar/17 $$\:\frac{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{7}/\mathrm{3}} }{\mathrm{7}}−\frac{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{4}/\mathrm{3}}…

Question Number 11146 by suci last updated on 14/Mar/17 $$\int {sin}^3(1+2x)dx=\dots .???$$ Answered by ajfour last updated on 14/Mar/17 $$=-\frac{3}{8}\cos (2x+1)+\frac{1}{24}\cos (6x+3)+C$$ Commented by…

Question Number 76661 by john santu last updated on 29/Dec/19 $$calculate\int \frac{x^2-2}{(x^4+5x^2+4)arc\tan \left(\frac{x^2+2}{x}\right)}dx$$ Answered by benjo 1/2 santuyy last updated on…

Question Number 142191 by iloveisrael last updated on 27/May/21 Commented by Mathspace last updated on 27/May/21 $$whytan\left(\frac{x}{2}\right)=i+\frac{2i}{1+e^{ix}}?$$$$andwhatisvalueof{\int }_0^{2\pi }\frac{sin\left(nx\right)}{1+e^{ix}}dx$$$${all}\:{this}\:{need}\:{proof}……

Question Number 142149 by cesarL last updated on 27/May/21 $$6.\int \frac{dx}{x^2-3x+2}$$$$7.\int \frac{4dx}{x^2+2x+4}$$$$8.\int \frac{3-2xdx}{x^2-64}$$$$9.\int \frac{3x-1}{x^3+5x^2+6x}dx$$$$\mathrm{10}.\:\int\frac{\mathrm{4}−\mathrm{3}{x}}{{x}^{\mathrm{3}} −\mathrm{2}{x}}{dx} \…