- #1

- 48

- 0

I am trying to find the integral of the following:

[tex]\int\left({\frac{3 + 5x - 6x^2 - 7x^3}{2x^2}}\right)dx[/tex]

What I did was to split up the fraction like so:

[tex]\int\left({\frac{3}{2x^2}}\right)dx + \int\left({\frac{5x}{2x^2}}\right)dx + \int\left({\frac{6x^2}{2x^2}}\right)dx + \int\left({\frac{7x^2}{2x^2}}\right)dx [/tex]

Simplified the fractions, worked out each integral then added them to get:

[tex]-\frac{3}{2x} + \frac{5}{2}\ln x - 3x - \frac{7}{4}x^2 + c[/tex]

The text I am using has no answers and when I tried to use the integral calculator at http://www.numberempire.com/integralcalculator.php I get an answer that is a fraction.

Am I correct and is the process I used to solve this correct?

Thanks.

[tex]\int\left({\frac{3 + 5x - 6x^2 - 7x^3}{2x^2}}\right)dx[/tex]

What I did was to split up the fraction like so:

[tex]\int\left({\frac{3}{2x^2}}\right)dx + \int\left({\frac{5x}{2x^2}}\right)dx + \int\left({\frac{6x^2}{2x^2}}\right)dx + \int\left({\frac{7x^2}{2x^2}}\right)dx [/tex]

Simplified the fractions, worked out each integral then added them to get:

[tex]-\frac{3}{2x} + \frac{5}{2}\ln x - 3x - \frac{7}{4}x^2 + c[/tex]

The text I am using has no answers and when I tried to use the integral calculator at http://www.numberempire.com/integralcalculator.php I get an answer that is a fraction.

Am I correct and is the process I used to solve this correct?

Thanks.

Last edited: