Integration by substitution b

Integration is the :

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

Let alpha in (0, pi/2) be fixed. If the integral int(tan x + tan alpha)/(tan x - tan alpha)dx = A(x)cos 2 alpha+B(x) sin 2 alpha +C ,where C is a constant of integration, then the functions A(x) and B(x) are respectively.

Integrate: 1/x^2-a^2 dx. Integrate: 1/a^2-x^2 dx . Integration of : 1/x^2-a^2 dx. Integration of : 1/a^2-x^2 dx . Integration most important questions.

Integrate the functions sqrt(a x+b)

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