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How do I evaluate the indefinite integral #intsec^2(x)*tan(x)dx# ?

Answer 1

Aurora Alvarado

The answer is #=1/2sec^2x+C#

Complete this integral by using a substitute.

Let #u=sec^2x#, #=>#, #du=2sec^2xtanxdx#

Consequently, the integral is

#I=intsec^2xtanxdx=1/2intdu#

#=1/2u#

#=1/2sec^2x+C#

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Answer 2

Christopher Allers

To evaluate the indefinite integral ∫sec^2(x) * tan(x) dx, you can use the substitution method. Let u = sec(x), then du = sec(x) * tan(x) dx. The integral becomes ∫du. Integrating du gives u + C. Substituting back, the result is sec(x) + C. Therefore, the indefinite integral of sec^2(x) * tan(x) dx is sec(x) + 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.