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How do you find the integral of #int tan^(7)xsec^(2)xdx#?

Answer 1

Emily Ammerman

If you can't integrate straight away, try substitution.

Can we turn this into #int u^n du#?

Hint: What is the derivative of #tanx#?

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Answer 2

Ezra Adams

To find the integral of ∫ tan^7(x)sec^2(x) dx, you can use trigonometric identities and integration by substitution. You can rewrite tan^7(x) as (sec^2(x) - 1)^7 sec^2(x) and then substitute u = sec(x) - 1. This will simplify the integral into a form that can be more easily integrated. After integration, you can then substitute back for sec(x) to obtain the final result.

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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.