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Category: Integration

nice-calculus-n-2-n-n-4-n-

Question Number 141082 by mnjuly1970 last updated on 15/May/21 $$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:……..\:{nice}\:\:…….\:\:{calculus}\:…….. \\ $$$$\:\:\:\boldsymbol{\phi}:=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\:\frac{\zeta\:\left(\:{n}\:\right)}{{n}\:.\:\mathrm{4}^{{n}} }=? \\ $$$$ \\ $$ Answered by mindispower last…

Question-75512

Question Number 75512 by Master last updated on 12/Dec/19 Commented by MJS last updated on 12/Dec/19 $$\mathrm{this}\:\mathrm{is}\:\mathrm{a}\:\mathrm{standard}\:\mathrm{integral};\:\mathrm{you}\:\mathrm{can}\:\mathrm{find}\:\mathrm{it}\:\mathrm{on} \\ $$$$\mathrm{any}\:\mathrm{table}\:\mathrm{of}\:\mathrm{integrals} \\ $$ Commented by JDamian last…

2-1-1-x-dx-

Question Number 9975 by Tawakalitu ayo mi last updated on 19/Jan/17 $$\int_{\:−\mathrm{2}\:} ^{\:−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:\mathrm{dx} \\ $$ Commented by prakash jain last updated on 20/Jan/17 $$\int\frac{\mathrm{1}}{{x}}{dx}=\mathrm{ln}\:{x}…

Evaluation-of-n-0-1-n-1-n-2-solution-1-n-1-1-n-n-2-i-2-1-2i-n-1-1-n-n-i-1-n-n-i-1-1-2i-

Question Number 140996 by mnjuly1970 last updated on 14/May/21 $$ \\ $$$$\:\:\:\:\:\:\mathscr{E}{valuation}\:{of}\:::\:\Omega\::=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{1}+{n}^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:{solution}:: \\ $$$$\:\:\:\:\:\Omega:=\mathrm{1}+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} −{i}^{\mathrm{2}} }\:=\frac{\mathrm{1}}{\mathrm{2}{i}}\left\{\underset{{n}=\mathrm{1}}…

1-x-5-1-dx-

Question Number 75446 by Crabby89p13 last updated on 11/Dec/19 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{5}} −\mathrm{1}}{dx} \\ $$ Answered by MJS last updated on 11/Dec/19 $$\mathrm{decomposing} \\ $$$$\int\frac{{dx}}{{x}^{\mathrm{5}} −\mathrm{1}}={I}_{\mathrm{1}} +{I}_{\mathrm{2}}…