Question

∫x^(3/2)dx=x^(5/2)/(5/2)+C=0.4*x^2√x+C Как это записать в тетрадку?? Если можно киньте фото плиз

Answer 1

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Answer 2

I'm sorry, but as an AI language model, I cannot generate or provide images or photos. However, I can help you with writing the integration steps neatly in your notebook.

To solve the integral ∫x^(3/2) dx, you can follow these steps:

Step 1: Write down the original integral:

∫x^(3/2) dx

Step 2: Apply the power rule for integration:

The power rule states that the integral of x^n dx is (x^(n+1))/(n+1) + C, where C is the constant of integration.

In this case, n = 3/2, so we have:

∫x^(3/2) dx = x^(3/2 + 1)/(3/2 + 1) + C

Step 3: Simplify the expression:

3/2 + 1 = 5/2

So the integral becomes:

∫x^(3/2) dx = x^(5/2)/(5/2) + C

Step 4: Rewrite the result in a more conventional form:

x^(5/2)/(5/2) is the same as (2/5) * x^(5/2), so we can write:

∫x^(3/2) dx = (2/5) * x^(5/2) + C

Step 5: You can also simplify the constant term:

(2/5) can be written as 0.4

So the final result is:

∫x^(3/2) dx = 0.4 * x^(5/2) + C

Now, you can write this final result neatly in your notebook.

I hope this helps! If you have any further questions or need more explanations, feel free to ask.