What is #int (x+7)dx#?

1 Answer
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Jan 28, 2017

#intx+7dx=x^2/2+7x+C#

Explanation:

The Fundamental Theorem of Calculus states

#intf(x)dx=F(x)+C# where #F'(x)=f(x)#

Since #(x^2/2)'=x# by the power rule #intxdx=x^2/2#

and since #intcdx=cintdx# then #int7dx=7intdx=7x#

And since the integral of a sum is the sum of integrals

#intx+7dx=x^2/2+7x+C#

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