How do you find the antiderivative of #f(x)=x^6#?

2 Answers
Jim G.
Nov 21, 2016

#1/7x^7+c#

Explanation:

Integrate using the #color(blue)"power rule for integration"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(intax^ndx=a/(n+1)x^(n+1))color(white)(2/2)|)))#

#rArrintx^6dx=1/7x^7+c#

where c is the constant of integration.

Brandon
Apr 15, 2018

#1/7x^7+C#

Explanation:

Antiderivitive means integration:

using the power rule for integration:

#int x^n dx =x^(n+1)/(n+1)+C#

#therefore# #int x^6 dx -> x^7/7+C -> 1/7x^7+C#

This is the final answer:

#1/7x^7+C#

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