Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 123964 by mindispower last updated on 29/Nov/20

$$\int \sqrt{x^3+ax+b}dx$$

Commented by MJS_new last updated on 29/Nov/20

$$x_1=p$$$$x_2=-\frac{p}{2}-\sqrt{q}$$$$x_3=-\frac{p}{2}+\sqrt{q}$$$$(x-x_1)(x-x_2)(x-x_3)=x^3+ax+b\Rightarrow$$$$a=-\frac{3p^2}{4}-q\wedge b=-\frac{p^3}{4}+pq$$$$\Rightarrow \mathrm{we}\mathrm{can}\mathrm{try}$$$$\int \sqrt{x-p}\sqrt{x^2+px+\frac{p^2}{4}-q}dx$$$$\mathrm{but}\mathrm{I}\mathrm{found}\mathrm{no}\mathrm{path}\mathrm{yet}$$

Commented by mindispower last updated on 30/Nov/20

$$thankyousirmetooihavenotfoundsomthing$$$$mybeethereisnoclose]formor$$$$somespecialfunctionwedontseeyet$$$$haveanicedaysir$$$$$$

Commented by MJS_new last updated on 30/Nov/20

$$\mathrm{Wolfram}\mathrm{Alpha}\mathrm{gives}\mathrm{super}\mathrm{complicated}$$$$\mathrm{solutions}\mathrm{for}\int \sqrt{x-p}\sqrt{x^2+px+\frac{p^2}{4}-q}dx$$$$\mathrm{and}\int \sqrt{x-p}\sqrt{x+\frac{p}{2}-\sqrt{q}}\sqrt{x+\frac{p}{2}+\sqrt{q}}dx,$$$$(\mathrm{for}\int \sqrt{x^3+ax+b}dx{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{also}\mathrm{including}\mathrm{the}$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$\mathrm{including}\mathrm{elliptic}\mathrm{functions}\mathrm{E}\mathrm{and}\mathrm{F};\mathrm{but}\mathrm{it}$$$$\mathrm{cannot}\mathrm{solve}\int \sqrt{x-a}\sqrt{x-b}\sqrt{x-c}\mathrm{at}\mathrm{all}.$$

Commented by mindispower last updated on 30/Nov/20

$$thankyousir$$$$isee$$$$\int \sqrt{x-a}.\sqrt{x^2\underset{-}{+}b}$$$$canbeesolvedby$$$$x=\sqrt{b}ch\left(t\right),wehen-$$$$x=\sqrt{b}sh\left(t\right),when+maybee$$$$thanxagainsir$$$$x=$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com