Antiderivative of anti-trigs(arctan)

Thread starter vipertongn
Start date Feb 23, 2009
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Antiderivative

In summary, the antiderivative of arctan is x + C, and can be found using the formula ∫tan(x)dx = x + C. This method can also be applied to other anti-trig functions, such as arcsin and arccos. There is a specific method for solving antiderivatives of anti-trigs, which involves using inverse trigonometric identities and integration by substitution. The antiderivative can be simplified using trigonometric identities and substitution, but it is important to always include the constant C in the final answer. Common mistakes to avoid when finding the antiderivative of anti-trigs include forgetting to include the constant, using the wrong inverse trigonometric identity, or not substituting

Feb 23, 2009

vipertongn

Homework Statement

arctan(x)/(1+x2). finding the antiderivative

Homework Equations

arctanx=1/1+x^2

The Attempt at a Solution

I tried pulling out arctan(x) S 1/(1+x^2) dx --> arctan^2(x)+c but the answer also has a 1/2 in front of the arctan...where'd that come from?

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Feb 23, 2009

Gib Z

Homework Helper

You can't just pull out the arctan! You can only pull out constants. Try making a u-substitution.

FAQ: Antiderivative of anti-trigs(arctan)

1. What is the antiderivative of arctan?

The antiderivative of arctan is simply x + C, where C is a constant. This can also be written as: ∫tan(x)dx = x + C.

2. How do you find the antiderivative of anti-trigs (arctan)?

To find the antiderivative of anti-trigs, such as arctan, you can use the following formula: ∫tan(x)dx = x + C. This formula can also be applied to other anti-trig functions, such as arcsin and arccos.

3. Is there a specific method for solving antiderivatives of anti-trigs (arctan)?

Yes, there is a specific method for solving antiderivatives of anti-trigs. It involves using the inverse trigonometric identities and integration by substitution. This method is also known as the "reverse chain rule."

4. Can the antiderivative of anti-trigs (arctan) be simplified?

Yes, the antiderivative of anti-trigs can be simplified by using trigonometric identities and substitution. It is important to note that the constant C should always be included in the final answer.

5. Are there any common mistakes to avoid when finding the antiderivative of anti-trigs (arctan)?

One common mistake to avoid is forgetting to include the constant C in the final answer. Another mistake is not using the correct inverse trigonometric identity or forgetting to substitute the correct variable after integration by substitution. It is important to carefully follow the steps and double-check the final answer for accuracy.