Dolly Robinson
2021-09-07
Answered

Determine whether the expression is true or false:

$\int \mathrm{tan}\left(2x\right)\times dx=-\frac{1}{2}\mathrm{ln}\times \left|\mathrm{cos}\left(2x\right)\right|+C$

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Luvottoq

Answered 2021-09-08
Author has **95** answers

Thus, the solution is true.

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I'm just learning about antiderivative that resulted some inverse trigonometric functions, since derivative of $\mathrm{arccos}(x)$ is $-\frac{1}{\sqrt{1-{x}^{2}}}$. I tried put this value back into integral calculator, but I got $-\mathrm{arcsin}(x)$ instead of $\mathrm{arccos}(x)$. even though $-\mathrm{arcsin}(x)\ne \mathrm{arccos}(x)$ so why this happen? How should I fix my understanding?

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