How do you find \int ( 2x + \frac { 3} { x ^ { 2} } ) d x(2x+3x2)dx?

1 Answer
Feb 5, 2017

int(2x+3/x^2)dx=x^2-3/x+C(2x+3x2)dx=x23x+C

Explanation:

Since int f(x)+g(x)dx=intf(x)dx+intg(x)dxf(x)+g(x)dx=f(x)dx+g(x)dx

We can say

int(2x+3/x^2)dx=int2xdx+int3/x^2dx(2x+3x2)dx=2xdx+3x2dx

Also since intcxdx=cintxdxcxdx=cxdx

we can say

int2xdx+3/x^2dx=2intxdx+3int1/x^2dx=2(x^2/2)-3(1/x)2xdx+3x2dx=2xdx+31x2dx=2(x22)3(1x)

Then

int(2x+3/x^2)dx=x^2-3/x+C(2x+3x2)dx=x23x+C