" If "2bar(sigma)" .3."(2x+1)/(sqrt(2x^(2)+x-3))" and "x" and "C_(1)+C_(2)=C_(1)

If (1+x)^(n) = overset(n)underset(r=0)Sigma C_(r)x^(r ) , then prove that C_(1)+2C_(2)+3C_(3)+…..+nC_(n)=n2^(n-1) .

If tan A= 1/(sqrt(x(x^2+x+1))), tan B = sqrtx/(sqrt (x^2+ x+ 1)) and tan C = sqrt(x^(-3)+x^(-2)+x^(-1)) , prove that A+B=C.

int(x^(3))/(sqrt(1+x^(2)))dx=a(1+x^(2))^((3)/(2))+b* sqrt(1+x^(2))+C

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n)," prove that " 1^(2)*C_(1) + 2^(2) *C_(2) + 3^(2) *C_(3) + …+ n^(2) *C_(n) = n(n+1)* 2^(n-2) .

Find the integral int(1)/(sqrt((1-x)(2-x)))dx A. log(2x-3)+sqrt((2x-3)^(2)-1)+Cquad B. log(2x-3)-sqrt((2x-3)^(2)+1)+C C. log(2x+3)-sqrt((2x+3)^(2)-1)+Cquad D. log(2x+3)+sqrt((2x+3)^(2)+1)+C

int sqrt (1 + x ^(2)). x dx = (1)/(3) (1 + x ^(2)) ^((3)/(2)) + c

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n)," prove that " + 3^(2) *C_(3) + …+ n^(2) *C_(n) 1^(2)*C_(1) + 2^(2) *C_(2) = n(n+1)* 2^(n-2) .

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+ . . .+C_(n)x^(n) , then the value of : C_(1)+2C_(2)+3C_(3)+ . . .+nC_(n) is:

IfI=int(dx)/((2a x+x^2)^(3/2)) ,then I is equal to (a) -(x+a)/(sqrt(2a x+x^2))+c (b) -1/a(x+a)/(sqrt(2a x+x^2))+c (c) -1/(a^2)(x+a)/(sqrt(2a x+x^2))+c (d) -1/(a^3)(x+a)/(sqrt(2a x+x^3))+c

IfI=int(dx)/((2a x+x^2)^(3/2)) ,then I is equal to (a) -(x+a)/(sqrt(2a x+x^2))+c (b) -1/a(x+a)/(sqrt(2a x+x^2))+c (c) -1/(a^2)(x+a)/(sqrt(2a x+x^2))+c (d) -1/(a^3)(x+a)/(sqrt(2a x+x^3))+c