`int x(ax+b)^(1/2)dx`

int(ax+b)^(2)dx

int x^(2)(ax+b)^(-2)dx is equal to

int(1)/((ax+b)^(2))dx

By substitution: Theorem: If int(ax+b)^(n)dx=((ax+b)^(n+1))/(a)(n+1)

Integrate the following functions w.r.t. x , (i) int(ax+b)^(n)dx (ii)int(2^((1)/(x)))/(x^(2))dx (iii) int(2dx)/((e^(x)+e^(-x))^(2)) (iv) (1)/(x^(2)(x^(4)+1)^((3)/(4))dx (v) int((tan^(-1)x)^(3))/(1+x^(2))dx

int 1/(ax+b) dx

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

By substitution: Theorem: If int f(x)dx=phi(x) then int f(ax+b)dx=(1)/(a)phi(ax+b)dx

Evaluate the following integrals. int (x dx)/(ax^(2) + b)^(p)

Evaluate: int(ax^(3/2)+be^x - 1/x)dx