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How do you evaluate the integral #intdx/(2x+3)#?

Answer 1

Isabella Ackerman

The answer is #==1/2ln(|2x+3|)+C#

We need

#intdx/x=lnx+C#

Let #u=2x+3#

#du=2dx#

#dx=du(1/2)#

#intdx/(2x+3)=1/2int(du)/u#

#=1/2lnu#

#=1/2ln(|2x+3|)+C#

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Answer 2

Samantha Adkison

To evaluate the integral ∫ dx / (2x + 3), you can use a technique called substitution. Let u = 2x + 3, then du/dx = 2, and solving for dx gives dx = du/2. Substitute u and du/2 into the integral, rewrite it in terms of u, and integrate with respect to u. After finding the antiderivative, revert back to x. The result is (1/2) * ln|2x + 3| + C, where C is the constant of integration.

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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.