Solving \int tan^{4}(x)dx Without a Table

TromboneNerd · 2010-05-11T15:38:36+00:00

how can i use u substitution to solve \int tan^{4}(x)dx? I am not allowed to use a table, so i can't use the \int tan^{n}(u)du formula. I have no work since i can't even make it fit \int udu. help?

Thread starter TromboneNerd
Start date May 11, 2010
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In summary, solving integrals without a table is possible through techniques such as integration by parts. This allows for a deeper understanding of integration and more flexibility in problem-solving. An example of solving ∫ tan4(x)dx without a table is through the substitution u = tan(x) and using integration by parts. Tips for solving integrals without a table include looking for substitutions, using integration techniques, and practicing regularly. However, not all integrals with trigonometric functions can be solved without a table, and it is important to have a strong understanding of integration techniques and when a table may be necessary.

May 11, 2010

TromboneNerd

how can i use u substitution to solve [tex]\int tan^{4}(x)dx[/tex]?

I am not allowed to use a table, so i can't use the [tex]\int tan^{n}(u)du[/tex] formula. I have no work since i can't even make it fit [tex]\int udu[/tex]. help?

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May 11, 2010

Cyosis

Homework Helper

Use the identity [itex]1+\tan^2x=\sec^2x[/itex].

FAQ: Solving \int tan^{4}(x)dx Without a Table

What is the method for solving ∫ tan4(x)dx without using a table?

The method for solving this integral is through a technique called integration by parts. This involves breaking down the integral into smaller parts and using a formula to solve each part.

Why is it important to be able to solve integrals without a table?

Solving integrals without a table allows for a deeper understanding of the underlying concepts and techniques of integration. It also allows for more flexibility in problem-solving and can be useful in situations where a table may not be readily available.

3. Can you provide an example of solving ∫ tan4(x)dx without a table?

Yes, an example of solving this integral without a table would be:

∫ tan4(x)dx = ∫ tan2(x) * tan2(x)dx

Using the substitution u = tan(x), the integral can be rewritten as:

∫ u2 * (1 + u2)dx

Using integration by parts, the integral can be solved as:

= (u3/3) + (u5/5) + C

= (tan3(x)/3) + (tan5(x)/5) + C

4. Are there any tips for solving integrals without a table?

Yes, some tips for solving integrals without a table include: looking for substitutions to simplify the integral, using integration by parts or other integration techniques, and practicing regularly to improve problem-solving skills.

5. Can integrals with trigonometric functions always be solved without a table?

Not always. While many integrals with trigonometric functions can be solved without a table using various techniques, there are some that may require the use of a table or other methods. It is important to have a strong understanding of integration techniques and to be able to recognize when a table may be necessary.