Questions: Compute the given integral. [ int frac1x^2+1 d x= ] +C

$Compute the given integral. [ int frac1x^2+1 d x= ] +C$

Transcript text: Compute the given integral. \[ \int \frac{1}{x^{2}+1} d x= \] $\square$ $+C$

Solution

Solution Steps

To solve the integral $\int \frac{1}{x^{2}+1} \, dx$, recognize that it is a standard integral that results in the arctangent function. The antiderivative of $\frac{1}{x^2 + 1}$ is $\arctan(x)$.

Step 1: Recognize the Integral Form

The integral $\int \frac{1}{x^2 + 1} \, dx$ is a standard form that corresponds to the derivative of the arctangent function.

Step 2: Identify the Antiderivative

The antiderivative of $\frac{1}{x^2 + 1}$ is $\arctan(x)$.

Final Answer

The integral evaluates to: \[ \boxed{\arctan(x) + C} \]

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