Primitive of Arctan x: Ideas & Solutions

Thread starter kidia
Start date May 2, 2005
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Function Primitive

In summary, the primitive of arctan x, also known as the antiderivative of arctan x, is a function that is the inverse of the derivative of arctan x. To find it, one can use the integration technique of substitution or the trigonometric identity arctan x = tan^-1(x). The primitive of arctan x and the integral of arctan x are essentially the same thing, and there is a general formula for it. This function is important in mathematics due to its use in various applications and its role in the process of integration.

May 2, 2005

kidia

Please any idea on this,find the primitive of arctan x

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May 2, 2005

Data

Two ways: Make the substitution u=arctan x, or use integration by parts,

[tex]\int u \ dv = uv - \int v \ du[/tex]

where dv=dx, u=arctan x (they really work out in the same way anyways).

May 2, 2005

kidia

Yah now I understand it will be the intergral of arctanxdx. thanx.

1. What is the definition of the primitive of arctan x?

The primitive of arctan x, also known as the antiderivative of arctan x, is a function that, when differentiated, gives the original function arctan x. In other words, it is the inverse of the derivative of arctan x.

2. How do you find the primitive of arctan x?

To find the primitive of arctan x, you can use the integration technique of substitution. This involves substituting u = arctan x and then using the formula for the primitive of u to find the primitive of arctan x. Alternatively, you can also use the trigonometric identity arctan x = tan^-1(x) to rewrite the function and then integrate using the power rule.

3. What is the relationship between the primitive of arctan x and the integral of arctan x?

The primitive of arctan x and the integral of arctan x are essentially the same thing. The integral of arctan x is another term for the primitive of arctan x, and both refer to the same function that is the inverse of the derivative of arctan x.

4. Is there a general formula for the primitive of arctan x?

Yes, there is a general formula for the primitive of arctan x. It is given by ∫arctan x dx = xarctan x - 1/2 ln(1+x^2) + C, where C is the constant of integration.

5. Why is the primitive of arctan x important in mathematics?

The primitive of arctan x is important in mathematics because it is a fundamental function that is used in many mathematical applications. It is also a key component in the process of integration, which is essential for solving many mathematical problems in various fields such as physics, engineering, and economics.