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