Find an antiderivative of in the variable x where x != 0

Question

Find an antiderivative of  3x^2+7x^4/x^5 in the variable x where x ≠ 0

Remember to include a "+ C" if appropriate.

 

Antiderivative = 

Answer 1

I will provide an alternative answer than the one provided by Mark here because the order of operations is unclear:

If ∫(3x² + 7x⁴/x⁵)dx, we can simplify the expression to ∫(3x² + 7/x)dx by canceling out the values in the numerator and denominator leaving only x in the denominator. This simplifies the integral to: 3∫x² dx+ 7∫(1/x)dx = x³ + 7log(x) + C

Otherwise, if the value x⁵ is distributed to all values in the numerator, then Marks response should be referenced.

Answer 2

∫ [ (3x² + 7x⁴) / x⁵ ]dx = ∫ [3x^-3 + 7x^-1]dx = 3(x^-2/(-2)) + 7 ln lxl + C

Answer 3

Here you go! Hope this helps!