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How do you evaluate the indefinite in integral? Use C for constant integration

#int(2+4x)/(1+x^2)dx#

Answer 1

Charles Arocha

#int (2+4x)/(1+x^2) dx = 2arctanx + 2ln(1+x^2) +C#

Using the linearity of the integral:

#int (2+4x)/(1+x^2) dx = 2int dx/(1+x^2) + 2 int (2xdx)/(1+x^2)#

#int (2+4x)/(1+x^2) dx = 2arctanx + 2 int (d(1+x^2))/(1+x^2)#

#int (2+4x)/(1+x^2) dx = 2arctanx + 2ln(1+x^2) +C#

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Answer 2

Axel Alvarez

To evaluate an indefinite integral, you apply the antiderivative rules and then add a constant of integration, typically denoted as ( C ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.