Help with Indefinite integrals.

In summary, an indefinite integral is a mathematical expression used to find the original function when only the derivative is known. To solve it, one can use integration techniques or seek help from a math tutor. The main difference between indefinite and definite integrals is that the latter gives a numerical value while the former represents a family of functions. Some common mistakes when solving indefinite integrals include forgetting to add the constant of integration and making algebraic errors. To check if the solution is correct, one can take the derivative of the antiderivative or use online calculators.
  • #1
master1425
5
0

Homework Statement


[tex]\int sinx/(1+cos^{2}x)dx [/tex]


Can anyone help me with this problem?
 
Last edited:
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  • #2
Did you try substituting u=cos(x) as a first step??
 
  • #3
Ah ok, that was my biggest problem. I tried substituting u=1+cos^2x and u=sinx. But neither yielded the result I wanted.

So I will try using just u=cosx and see how that works for me.
 
  • #4
Ok, I got that one finally.

How about this one?

[tex]\int x^{2}sinx/1+x^{6} dx [/tex]

I tried u=sinx, but got stuck. Is that what I need to use? Any help would be appreciated.
 

What is an indefinite integral?

An indefinite integral is a mathematical expression that represents the antiderivative of a function. It is used to find the original function when only the derivative is known.

How do I solve an indefinite integral?

To solve an indefinite integral, you need to use integration techniques such as substitution, integration by parts, or trigonometric substitution. You can also use online integration calculators or consult with a math tutor for help.

What is the difference between definite and indefinite integrals?

A definite integral has specific limits of integration, which means that it gives a numerical value as the result. In contrast, an indefinite integral has no limits of integration, so it represents a family of functions that differ by a constant.

What are some common mistakes when solving indefinite integrals?

Some common mistakes when solving indefinite integrals include forgetting to add the constant of integration, making errors in algebraic manipulations, and missing a negative sign. It is essential to double-check your work to avoid these mistakes.

How can I check if my solution to an indefinite integral is correct?

You can check your solution by taking the derivative of the antiderivative you found. If the result matches the original function, your answer is correct. You can also use online integral calculators to verify your solution.

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