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Category: Integration

2-x-2-1-x-1-x-2-dx-

Question Number 91086 by jagoll last updated on 28/Apr/20 $$\int\:\frac{\mathrm{2}−{x}^{\mathrm{2}} }{\mathrm{1}+{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:{dx}\: \\ $$ Answered by MJS last updated on 28/Apr/20 $$\int\frac{\mathrm{2}−{x}^{\mathrm{2}} }{\mathrm{1}+{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}= \\…

0-1-arcsin-x-x-dx-

Question Number 156616 by amin96 last updated on 13/Oct/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{arcsin}\left({x}\right)}{{x}}{dx}=? \\ $$ Answered by mindispower last updated on 13/Oct/21 $${by}\:{part}=−\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({x}\right)}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}…

this-trig-integral-has-quite-a-few-insights-on-trig-integrals-andd-u-subs-as-well-as-on-the-properties-of-logarithms-try-it-out-it-s-a-nice-one-tan-x-dx-

Question Number 91074 by  M±th+et+s last updated on 27/Apr/20 $${this}\:{trig}\:{integral}\:{has}\:{quite}\:{a}\:{few}\: \\ $$$${insights}\:{on}\:{trig}\:{integrals}\:{andd}\: \\ $$$${u}\:{subs}\:{as}\:{well}\:{as}\:{on}\:{the}\:{properties} \\ $$$${of}\:{logarithms}.\:{try}\:{it}\:{out}\:{it}'{s}\:{a}\:{nice} \\ $$$${one} \\ $$$$\int{tan}\left({x}\right){dx} \\ $$ Commented by mathmax…

Question-91054

Question Number 91054 by Mikael_786 last updated on 27/Apr/20 Commented by MJS last updated on 27/Apr/20 $$\mathrm{I}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{integral}\:\int\omega^{\mathrm{1}/{x}} {dx}\:\mathrm{but}\:\mathrm{I}\:\mathrm{cannot} \\ $$$$\mathrm{solve}\:\mathrm{the}\:\mathrm{limit}.\:\mathrm{it}\:\mathrm{seems}\:\:{L}=\mathrm{1} \\ $$ Commented by MJS…

hi-every-one-what-is-the-scientific-reason-for-using-trigonometric-compensation-in-integration-and-what-is-the-rule-that-we-rely-on-in-other-compensation-a-2-x-2-x-a-sin-OR-a-cos-

Question Number 91037 by  M±th+et+s last updated on 27/Apr/20 $${hi}\:{every}\:{one} \\ $$$${what}\:{is}\:{the}\:{scientific}\:{reason}\:{for}\:{using} \\ $$$${trigonometric}\:{compensation}\: \\ $$$${in}\:{integration}? \\ $$$${and}\:{what}\:{is}\:{the}\:{rule}\:{that}\:{we}\:{rely}\:{on} \\ $$$${in}\:{other}\:{compensation}? \\ $$$$ \\ $$$$\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}}…