`int2xa^(x^2)dx`

int2x.e^(x^(2))dx equal to

Evaluate: lim_(x->oo)((int_0^xe^(x^2)dx)^2)/(int_0^x e^(2x^2)dx)

Iff(2-x)=f(2+x)a n df(4-x)=f(4+x) for all xa n df(x) is a function for which int_0^2f(x)dx=5,t h e nint_0^(50)f(x)dx is equal to 125 (b) int_(-4)^(46)f(x)dx int_1^(51)f(x)dx (d) int_2^(52)f(x)dx

Evaluate the following integrals: (i) int 2x sqrt(1 + x^2)dx " " (ii) int e^(-x^2) x dx " " (iii) int (sin x)/(1 + cos x) dx (iv) int 1/(1 + x^2)dx " " (v) int x (a - x)^8 dx .

int_(2-a)^(2+a)f(x)dx is equal to [where f(2-alpha)=f(2+alpha) AAalpha in R] (a) 2 int_2^(2+a)f(x)dx (b) 2int_0^af(x)dx (c) 2int_2^2f(x)dx (d) none of these

(i) int(dx)/(sqrt(a^(2)-x^(2)))=(1)/(a)sin^(-1)((x)/(a))+c (ii) int(dx)/(a^(2)+x^(2))=tan^(-1)((x)/(a))+c (iii) int(x+1)/(x^(2)+2x+1)dx=(1)/(2)log|(x^(2)+2x+1)| (iv) int(dx)/(x(x-1))dx=log|(x-1)/(x)|+c State which pair of the statement given above is true.

int x/(1+x^(2))dx = …………………

int(x)/(e^(x^(2)))dx

Evaluate int(2x)/(x^(4)+x^(2)+1)dx