How do you integrate #int(3x^53)^(3/5)*15x^4 dx# using substitution?
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To integrate ( \int (3x^5  3)^{\frac{3}{5}} \cdot 15x^4 , dx ) using substitution:

Let ( u = 3x^5  3 ).

Find ( \frac{du}{dx} ) by taking the derivative of ( u ) with respect to ( x ).

Solve for ( dx ) in terms of ( du ).

Rewrite the integral in terms of ( u ) using the substitution ( u = 3x^5  3 ).

Integrate the new expression with respect to ( u ).

Replace ( u ) with ( 3x^5  3 ) in the result.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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