piquad " & "(bx^(2)+mx+n)/(sqrt(x))

What is the value of x, if (b+ sqrt(b^(2) - 2bx))/(b-sqrt(b^(2) - 2bx))=a?

lim_(x rarr1^(-))(sqrt(pi)-sqrt(2sin^(-1)x))/(sqrt(1-x))=(A)sqrt((2)/(pi))(B)sqrt((pi)/(2))(C)(1)/(pi)(D)sqrt((1)/(pi))

int_( then the value n+lambda is )^( If )(dx)/(sqrt(x^(2)+4x+3))dx=(lx^(2)+mx+n)sqrt(x^(2)+4x+3)+lambda int(dx)/(sqrt(x^(2)+4x+3))

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 int(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 int(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

Find the integral int(1)/(sqrt(a^(2)+b^(2)x^(2)))dx],[" A."(1)/(b)log bx+sqrt(a^(2)+b^(2)x^(2))|+Cquad " B."(1)/(b)log bx-sqrt(a^(2)+b^(2)x^(2))|+C],[" C."(1)/(a)log bx+sqrt(a^(2)+b^(2)x^(2))|+Cquad " D."(1)/(a)log bx-sqrt(a^(2)+b^(2)x^(2))|+C]

If the value of the definite integral int_(0)^(1)(sin^(-1)sqrt(x))/(x^(2)-x+1)dx is (pi^(2))/(sqrt(n)) (where n in N), then the value of (n)/(27) is