What is the antiderivative of a polynomial?

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Answer 1 · 2014-10-17T01:22:40

Let

#f(x)=a_nx^n+a_{n-1}x^{n-1}+cdots+a_1x+a_0#.

An antiderivative #F(x)#of #f(x)# can be found by

#F(x)=int f(x)dx#

#=int(a_nx^n+a_{n-1}x^{n-1}+cdots+a_1x+a_0)dx#

#=a_n/{n+1}x^{n+1}+a_{n-1}/nx^n+cdots+a_1/2x^2+a_0x+C#.

I hope that this was helpful.