int(1-x)(4-3x)(3+2x)dx,x in R

Evaluate: (i) int(5x^(2) + 2x^(-5) - 7x + 1/(sqrt(x)) +5/x) dx (ii) int(3sinx - 4 cosx + 5 sec^(2) x - 2cosec^(2)x) dx (iii) int(1-x)(2+3x)(5-4x)dx (iv) int((3x^(4) - 5x^(3) + 4x^(2) -x + 2)/(x^(3)))dx , (v) int(x^(2) + 1/(x^(2)))^(3) dx

int_(1)^(4)(3x^(2)+2x)dx

int(2x)/(4-3x-x^2)dx=

Evaluate the integerals. int (x^(2)+3x-1)/(2x) dx, x in I sub R\\{0}

int(x^4-3)/(x^2+2x+1)dx

int(1)/(2x^(2)+3x-4)dx

int(1)/((2-3x)^(2)(4-5x))dx=

int(3x+2)/((x-1)(2x+3))dx

A continous function f(x) is such that f(3x)=2f(x), AA x in R . If int_(0)^(1)f(x)dx=1, then int_(1)^(3)f(x)dx is equal to

I=int(2x^(3)+4x+1)/(x)dx