Need confirmation on this integration problem

• jzq
In summary, the conversation was about an integral problem involving e^(5x) and the correct solution being 1/5 * e^(5x) + c. The concept of linearity of primitive functions was also mentioned, stating that the integral of f(ax) is equal to 1/a * F(ax) + c. It was also mentioned to be careful with the variable of integration, as it may not always be dx.
jzq
Here's the problem:
$$\int e^{(5x)}$$

This is what I got (Correct me if I am wrong.):
$$\frac{1}{5}e^{(5x)}$$

Or is it just the same:
$$e^{(5x)}$$

jzq said:
Here's the problem:
$$\int e^{(5x)}$$

This is what I got (Correct me if I am wrong.):
$$\frac{1}{5}e^{(5x)}$$

Or is it just the same:
$$e^{(5x)}$$

You are sort of right. I think you mean

$$\int e^{(5x)}dx = \frac{1}{5}e^{(5x)} + c$$

Yes, I forgot to add the constant, but that's what I meant.
So I am correct then?

Yeah. In general, if you want to check yourself, just take the derivative of what you just integrated. If you get back the integrand, then you know you solved it correctly.

jzq said:
Here's the problem:
$$\int e^{(5x)}$$

This is what I got (Correct me if I am wrong.):
$$\frac{1}{5}e^{(5x)}$$

Or is it just the same:
$$e^{(5x)}$$

Linearity of primitive functions:

$$\int f(x)\ dx = F(x)\ +\ C \Rightarrow \int f(ax)\ dx = \frac{1}{a} F(ax)\ +\ C,\ a \in \mathbb{R}\ \backslash \ \{0\}$$

Thanks guys!

jzq said:
Yes, I forgot to add the constant, but that's what I meant.
So I am correct then?

You also forgot to include the variable of integration for your integral. You need to know what the integration variable is. It will not always be dx, so you should be careful with it.

1. What is an integration problem?

An integration problem is a mathematical problem that involves finding the integral (or the area under a curve) of a given function. It is commonly encountered in calculus and physics.

2. How do I know if my solution to an integration problem is correct?

You can confirm your solution by taking the derivative of your answer and verifying that it matches the original function.

3. What are some common techniques for solving integration problems?

Some common techniques for solving integration problems include substitution, integration by parts, and trigonometric substitutions.

4. Can integration problems have multiple solutions?

Yes, integration problems can have multiple solutions, depending on the given function and the chosen method of integration.

5. How can I improve my skills in solving integration problems?

Practicing regularly and familiarizing yourself with different integration techniques can help improve your skills in solving integration problems. Additionally, seeking guidance from a teacher or tutor can also be beneficial.

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