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Category: Integration

Question-118710

Question Number 118710 by eric last updated on 19/Oct/20 Answered by mathmax by abdo last updated on 19/Oct/20 $$\mathrm{M}=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }\mathrm{dx}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{lnx}}{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }\mathrm{dx}\:+\int_{\mathrm{1}}…

Question-118679

Question Number 118679 by Algoritm last updated on 19/Oct/20 Answered by 1549442205PVT last updated on 19/Oct/20 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\left[\mathrm{2x}\right].\mathrm{x}}{\left[\mathrm{2x}\right]+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}=\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\left[\mathrm{2x}\right].\mathrm{x}}{\left[\mathrm{2x}\right]+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}+\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \frac{\left[\mathrm{2x}\right].\mathrm{x}}{\left[\mathrm{2x}\right]+\mathrm{x}^{\mathrm{2}}…