" 1.(i) "int_(2)^(3)x^(2)dx" [NCERT] "

int(x^(3)-x^(2)+x-1)/(x-1)dx[NCERT

" (i) "int_(0)^(3)(dx)/((x+2)sqrt(1+x))

Evaluate : (i) int_(0)^(1)x(1-x)^(n)dx (ii) int_(0)^(1)x(1-x)^(3//2)dx

I=int(1)/(x^(3)+x^(2)+x+1)dx

If I_(1) = int_(0)^(1) 2^(x^(2))dx, I_(2) = int_(0)^(1) 2^(x^(3))dx , I_(3) = int_(1)^(2) 2^(x^(2))dx, I_(4)=int_(1)^(2) 2^(x^(3))dx then

Evaluate : (i) int(2x)/((2x+1)^(2))dx (ii) int((2+3x))/((3-2x))dx

Evaluate : (i) int(3x^(2))/((1+x^(6)))dx (ii) int(x^(3))/((x^(2)+1)^(3))dx (iii) (x^(8))/((1-x^(3))^(1//3))dx

Match the following : {:(" LIST - I","LIST - II"),("I)" int_(0)^(2)|1-x|dx=,"a) " 1),("II)" int_(0)^(2)|x-2|dx=,"b) "2),("III)" int_(0)^(2)(|x|+|x-1|)dx=,"c) "3):}

If I_(1)=int_(0)^(1) 2^(x^(2)) dx, I_(2)=int_(0)^(1) 2^(x^(3)) dx, I_(3)=int_(1)^(2) 2^(x^(2))dx and I_(4)=int_(1)^(2) 2^(x^(3))dx then