# How do you integrate #y=3 (5x+9)^9#?

Do a "u" substitution. Please see the explanation.

Reverse the substitution:

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To integrate the function y = 3(5x + 9)^9, you can use the substitution method. Let u = 5x + 9. Then, du/dx = 5. Rearrange to solve for dx: dx = du/5.

Now substitute u = 5x + 9 and dx = du/5 into the integral:

∫3(5x + 9)^9 dx = ∫3u^9 (1/5) du.

Now integrate with respect to u:

∫3u^9 (1/5) du = (3/5) ∫u^9 du.

Apply the power rule for integration:

(3/5) * (1/10) * u^10 + C = (3/50) * u^10 + C.

Now, substitute back for u:

(3/50) * (5x + 9)^10 + 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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