- #1
kidia
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Please any idea on this,find 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.
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.
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.
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.
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.