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Category: Integration

the-2-formulas-for-solving-dx-x-3-px-q-with-nasty-solutions-of-x-3-px-q-0-with-p-q-R-case-1-D-p-3-27-q-2-4-gt-0-x-3-px-q-0-has-got-1-real-and-2-conjugated-complex-solutions-u-

Question Number 68141 by MJS last updated on 06/Sep/19 the2formulasforsolvingdxx3+px+qwithnastysolutionsofx3+px+q=0withp,qRcase1D=p327+q24>0x3+px+q=0hasgot1real$$\mathrm{and}\:\mathrm{2}\:\mathrm{conjugated}\:\mathrm{complex}\:\mathrm{solutions}…

1-1-x-dx-

Question Number 133674 by liberty last updated on 23/Feb/21 1+1+xdx=? Answered by EDWIN88 last updated on 23/Feb/21 lety=1+1+x1+x=y21$$\Rightarrow\mathrm{1}+\sqrt{\mathrm{x}}\:=\:\mathrm{y}^{\mathrm{4}} −\mathrm{2y}^{\mathrm{2}} +\mathrm{1}\:,\:\mathrm{x}\:=\:\left(\mathrm{y}^{\mathrm{4}}…

dx-pi-e-x-2-1-x-

Question Number 68094 by mhmd last updated on 04/Sep/19 dx/(π+e)x2x Answered by MJS last updated on 05/Sep/19 $$\int\frac{{dx}}{\:\sqrt[{{x}}]{\left(\pi+\mathrm{e}\right)^{{x}^{\mathrm{2}} } }}=\int\frac{{dx}}{\left(\pi+\mathrm{e}\right)^{{x}} }=−\frac{\mathrm{1}}{\left(\pi+\mathrm{e}\right)^{{x}}…