How do you integrate #(6x7x^2) dx#?
where c is the constant of integration.
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To integrate ( \int (6x  7x^2) , dx ):

Use the power rule of integration, which states that ( \int x^n , dx = \frac{x^{n+1}}{n+1} + C ), where ( n \neq 1 ).

Integrate each term separately: [ \begin{align*} &\int (6x  7x^2) , dx \ &= \int (6x) , dx + \int (7x^2) , dx \ &= 6 \int x , dx  7 \int x^2 , dx \ \end{align*} ]

Apply the power rule to each term: [ \begin{align*} &=6 \left( \frac{x^2}{2} \right)  7 \left( \frac{x^3}{3} \right) + C \ &= 3x^2  \frac{7}{3}x^3 + C \ \end{align*} ]
So, ( \int (6x  7x^2) , dx = 3x^2  \frac{7}{3}x^3 + C ), where ( C ) is the constant of integration.
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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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