Question

indefinite integral of [(7x+3x^5+x^3)/x^3]dx

Answer 1

Divide each term of the numerator by x^3.

Answer 2

\[\int\limits \frac{(7x+3x^5+x^3)}{x^3}dx\]
?

Answer 3

divide by x^3 and convert to perfect sq

Answer 4

yes that is the right equation and can you explain how i am able to divide by x^3? I don't understand how i can do that

Answer 5

\[\Huge \int\limits\limits \frac{(\frac{7x}{x^3}+\frac{3x^5}{x^3}+\frac{x^3}{x^3})}{1}dx\]

Answer 6

so the 7x/x^3 would then be 7x^-2 ?

Answer 7

\[\Huge \int\limits\limits\limits \frac{(\frac{7}{x^2}+\frac{3x^2}{1}+1)}{1}dx\]
now try converting to perfect square

Answer 8

yep

Answer 9

thank you! :)

Answer 10

how do i convert to a perfect square?

Answer 11

or u can let x^2=t

Answer 12

If I may interject...that fraction can be simplified to the integral of 7/x^2 + 3x^2 + 1...and just integrate quickly (with the exception of the first one...but write first one as 7x^(-2). The other two is straightforward...x^3 and x, respectively. Why bother to change to a perfect square?