# How do you find the antiderivative of #f(x)= x^(3/4) + x^(4/3)#?

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To find the antiderivative of ( f(x) = x^{3/4} + x^{4/3} ), we can use the rules of integration. The antiderivative of ( x^n ) with respect to ( x ) is ( \frac{x^{n+1}}{n+1} ), except when ( n = -1 ), where the antiderivative is ( \ln|x| ).

Applying this rule to each term, we get:

( \int x^{3/4} , dx = \frac{4}{7} x^{7/4} )

( \int x^{4/3} , dx = \frac{3}{7} x^{7/3} )

So, the antiderivative of ( f(x) = x^{3/4} + x^{4/3} ) is ( \frac{4}{7} x^{7/4} + \frac{3}{7} x^{7/3} + C ), where ( C ) is the constant of integration.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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