Category: Integration

Question Number 31967 by abdo imad last updated on 17/Mar/18 $$findthevalueof{\int }_0^{\mathrm{\infty }}\frac{arctanx}{x^2+x+1}dx.$$ Commented by abdo imad last updated on 19/Mar/18 $${let}\:{put}\:{I}\:=\int_{\mathrm{0}}…

Question Number 163008 by tounghoungko last updated on 03/Jan/22 $$Calculate$$$$\int \frac{(2-4\sin x\cos x)(1+\sin 2x)}{\sin {}^{4}2x+64\cos {}^{4}2x}dx$$$$$$ Answered by som(math1967) last updated on 03/Jan/22…

Question Number 97417 by MJS last updated on 08/Jun/20 $$\int \frac{x}{a+{\sin }^{2}x}dx=?$$ Answered by MJS last updated on 08/Jun/20 $$\mathrm{just}\mathrm{found}\mathrm{a}\mathrm{path}:$$$$\mathrm{sin}\:{x}\:=\frac{\mathrm{e}^{\mathrm{i}{x}} −\mathrm{e}^{−\mathrm{i}{x}} }{\mathrm{2i}}…

Question Number 31858 by NECx last updated on 16/Mar/18 $$\int \frac{sinx}{x}dx$$ Commented by abdo imad last updated on 18/Mar/18 $${we}\:{have}\:{sinx}\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} \:}{\left(\mathrm{2}{n}+\mathrm{1}\right)!}\:{x}^{\mathrm{2}{n}+\mathrm{1}} \:\:{with}\:{radius}\:{R}=\infty…

Question Number 31838 by Joel578 last updated on 15/Mar/18 $$\mathrm{Given}$$$$f\left(x\right)=\frac{3}{16}\left({\int }_0^{1}f\left(x\right)dx\right)x^2-\frac{9}{10}\left({\int }_0^{2}f\left(x\right)dx\right)x+2\left({\int }_0^{3}f\left(x\right)dx\right)+4$$$$\mathrm{Solve}$$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}{t}\:+\:\left(\int_{{f}\left(\mathrm{2}\right)\:+\:\mathrm{2}} ^{{f}^{−\mathrm{1}}…