What is the antiderivative of $g(x) = x ^ π$ ?

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Answer 1 · 2016-05-26T13:06:23

$1/(pi+1)x^(pi+1) + C$

Don't let $pi$ throw you off. It's just a number. It's about 3.14.

What is the antiderivative of $x$ to a constant power? (of $x$ to a number?)

Add $1$ to the exponent and divide by the new exponent. (And don't forget to add the constant).

The antiderivative of $x^pi$ is $1/(pi+1)x^(pi+1) + C$

What is the antiderivative of g(x) = x ^ πg(x) = x ^ π?