Q:
# What Formula Do You Use for the Integral of Inverse Tangent?

The formula for the integral of inverse tangent is the integral of arctan(x) dx = x * arctan(x) - (1/2) * ln |x2+1|+ C. The integral is solved using integration by parts, which notes that the integral of u dv is equal to u times v minus the integral of v du. The term arctan represents the inverse function in mathematical formulas.

Continue ReadingUsing integration by parts for the integral of inverse tangent, the variable u is set to arctan(x), which means that the derivative of u, expressed as du, is set to 1/((x^2)+1). The derivative dv is set to dx, which when integrated, sets v equal to x. The integral of arctan(x) is rewritten as x * arctan(x) minus the integral of x/((x^2) + 1) dx. Integrating v du gives u = (x^2) + 1. The derivative of u, du, is 2xdx, from which the formula x dx = du/2 can be derived.

From those values, the integral of (x/(x^2) + 1) dx is evaluated as 1/2u du = (1/2) ln |u| = (1/2) ln |(x^2) + 1|. In these formulas, the line symbols indicate an absolute value that is neither positive nor negative. For the final solution, x * arctan(x) - (1/2) * ln |x2+1|+ C, C represents the constant of integration.

Learn more about Calculus-
Q:
## What Is the Integral of Arctan?

A: The integral of arctan is x times the inverse tangent of x, minus one-half of the natural logarithm of one plus x squared, plus the constant expressed as C... Full Answer >Filed Under: -
Q:
## What Is the Equation for Inverse Variation?

A: The general formula for inverse variation is k equals y times x, where k is a constant quantity, y is one variable and x is another variable. Under inverse... Full Answer >Filed Under: -
Q:
## What Is the Antiderivative of Tan?

A: The antiderivative of the tangent of x equals the negative natural log of the absolute value of the cosine of x, plus a constant. In mathematical terms, th... Full Answer >Filed Under: -
Q:
## What Is the Integral of Sqrt X 2 Y 2?

A: The indefinite integral of sqrt(x^2y^2) with respect to x is x^2y/2 + c, assuming that x and y are independent variables. The definite integral of this fun... Full Answer >Filed Under: