Determine whether the expression is true or false: ∫tan⁡(2x)×dx=−12ln×|cos⁡(2x)|+C

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High School
Calculus and Analysis
Calculus 1
Integrals

Dolly Robinson

Answered question

2021-09-07

Determine whether the expression is true or false:

\int \tan (2 x) \times d x = - \frac{1}{2} \ln \times | \cos (2 x) | + C

Answer & Explanation

Luvottoq

Skilled2021-09-08Added 95 answers

$\int \tan (2 x) \times d x = - \frac{1}{2} \ln \times | \cos (2 x) | + C$
$I = \int \tan (2 x) \times d x, s u b s t i t u t e 2 x = t, d x = d t$
$I = \frac{1}{2} \int \tan (t) d t$
$I = \frac{1}{2} \ln | \sec (x) | + C, \sec (x) = \frac{1}{\cos (x)} = {(\cos (x))}^{- 1},$
$I = - \frac{1}{2} \ln | \cos (x) | + C .$
Thus, the solution is true.

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