# How do you find the antiderivative of #int sinx/cos^3x dx#?

The answer is

We need

We perform this integral by substitution

Therefore,

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To find the antiderivative of ∫(sinx/cos^3x) dx, you can use the substitution method. Let u = cos(x), then du = -sin(x) dx. Substituting, the integral becomes ∫-1/(u^3) du. Integrating, you get (-1/(-2u^2)) + C = 1/(2u^2) + C. Substituting back for u, you get 1/(2cos^2(x)) + C. So, the antiderivative of the given expression is 1/(2cos^2(x)) + C.

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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.

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.

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.

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