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Evaluate the indefinite integral.$\int \frac{1+x}{1+x^{2}} d x$
$\tan ^{-1} x+\frac{1}{2} \ln \left(1+x^{2}\right)+C$
Calculus 1 / AB
Calculus 2 / BC
Chapter 5
Integrals
Section 4
The Substitution Rule
Integration Techniques
Baylor University
University of Michigan - Ann Arbor
Idaho State University
Lectures
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Evaluate the indefinite in…
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Evaluate the indicated int…
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Evaluate the integral.
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Evaluate the definite inte…
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this question asks us to evaluate the intro. We have one plus X over one plus X squared DX. The first step is we should write this in two parts. In other words, let's write this as 1/1 plus X squared DX plus X could remember it's one plus X There were doing one then plus acts over one prospect squared DX. This is a lot easier. And the reason why we're doing this is because one over you squared plus one D'You is inverse tangent of you and do you over you. The integral of that is natural log of you pussy. Therefore, we have the inverse tangent of acts. We're back substituting in. In the end, we don't want you. We want X plus 1/2 times the natural log of one plus x squared, which was the dump denominator and then plus seek
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