I'm having a problem figuring out the difference in terms of an anti-derivative and integral. The problem is:

Question

I'm having a problem figuring out the difference in terms of an anti-derivative and integral.  The problem is:

anonymous · Answer

Anti-derivatives are used to solve integrals.

anonymous · Answer

$$\int\limits_{}^{} \frac{ x dx }{ (7x^2+3)^5 }$$

I'm given this problem on two equations.  One asks for me to evaluate the integral and the other asks me to find the anti-derivative.  Using the sub method, I get 

$$-\frac{ 1 }{ 56 }(7x^2+3)^(-4)+ C$$ for both problems.  Can someone explain to me what I'm doing wrong

anonymous · Answer

Uhh.  That should be negative 1/56 times( 7x to the 2nd power + three in parentheses to the negative 4th power) + C

anonymous · Answer

Evaluating an improper integral is just finding the anti-derivative.

miracrown · Answer

Your result here is correct. Note that integral and anti-derivative are synonyms.

miracrown · Answer

You then correctly made use of a U substitution to do the integral.

anonymous · Answer

Thanks!  I'll keep in mind that the two are synonyms.  That really helped.  Appreciate the help from both of you!

miracrown · Answer

yw :)

anonymous · Answer

They aren't synonymous, they are just closely related.