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Euler's substitution: Integrals of th...

Euler's substitution:
Integrals of the form `intR(x, sqrt(ax^(2)+bx+c))dx` are claculated with the aid of one of the following three Euler substitutions:
i. `sqrt(ax^(2)+bx+c)=t+-x sqrt(a)if a gt 0`
ii. `sqrt(ax^(2)+bx+c)=tx+-x sqrt(c)if c gt 0`
iii. `sqrt(ax^(2)+bx+c)=(x-a)t if ax^(2)+bx+c=a(x-a)(x-b)` i.e., if `alpha` is real root of `ax^(2)+bx+c=0`
`int(xdx)/((sqrt(7x-10-x^(2)))^(3))` can be evaluated by substituting for x as

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Euler's substitution: Integrals of the form intR(x, sqrt(ax^(2)+bx+c))dx are claculated with the aid of one of the following three Euler substitutions: i. sqrt(ax^(2)+bx+c)=t+-x sqrt(a)if a gt 0 ii. sqrt(ax^(2)+bx+c)=tx+-x sqrt(c)if c gt 0 iii. sqrt(ax^(2)+bx+c)=(x-a)t if ax^(2)+bx+c=a(x-a)(x-b) i.e., if alpha is real root of ax^(2)+bx+c=0 (xdx)/(sqrt(7x-10-x^(2))^3) can be evaluated by substituting for x as

Euler's substitution: Integrals of the form intR(x, sqrt(ax^(2)+bx+c))dx are claculated with the aid of one of the following three Euler substitutions: i. sqrt(ax^(2)+bx+c)=t+-x sqrt(a)if a gt 0 ii. sqrt(ax^(2)+bx+c)=tx+-x sqrt(c)if c gt 0 iii. sqrt(ax^(2)+bx+c)=(x-a)t if ax^(2)+bx+c=a(x-a)(x-b) i.e., if alpha is real root of ax^(2)+bx+c=0 (xdx)/(sqrt(7x-10-x^(2))^3) can be evaluated by substituting for x as

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