# How do you evaluate the integral #int8x+3 dx#?

##### 1 Answer

When taking integrals, you will normally solve them one term at a time. You will do the inverse of the power rule so the answer would be:

#F(x) = 4x^2 + 3x + C#

Integrals are the inverse of derivatives so you follow the rules in reverse. The

#f(x) = x^n# then#f'(x)=nx^(n-1)#

To reverse the power rule, you will first add one to the exponent then divide the whole term by the new term:

#F(x) = (x^(n+1))/(n+1)#

Both terms in this problem can be solved with the power rule.

Due to this being a indefinite integral, not having any bounds, you will have to put

#f(x) = 6x^3 + 5# and#g(x) = 6x^3 + 25#

would have the same derivative because the constant becomes zero and the additive identity property states that anything added to zero is unchanged.