Key to "How to integrate cos2(2x)?"

Name: How to integrate cos2(2x)?
Uploaded: 2022-02-23T17:22:57+00:00
Description: How to integrate cos2(2x)?

Ayaana Buck

Answered question

2021-03-12

How to integrate

\cos^{2} (2 x)

Answer & Explanation

2k1enyvp

Skilled2021-03-13Added 94 answers

I = integral

I \cos^{2} (2 x) d x = (\frac{1}{2}) I \cos^{2} (t) d t

2 x = t, 2 d x = d t, d x = \frac{d t}{2}

I \cos^{2} (t) d t = I \cos t \cos t d t

u = \cos t, d u = - \sin t

d v = \cos t d t, v = \sin t

I \cos^{2} (t) d t = \sin t \cos t + I \sin^{2} (t) d t

I \cos^{2} (t) d t = \frac{\sin (2 t)}{2} + I (1 - \cos^{2} (t)) d t

I \cos^{2} (t) d t = \frac{\sin (2 t)}{2} + I d t - I \cos^{2} (t) d t

I \cos^{2} (t) d t + I \cos^{2} (t) d t = \frac{\sin (2 t)}{2}

2 I \cos^{2} (t) d t = \frac{\sin (2 t)}{2} + t

I \cos^{2} (t) d t = \frac{\sin (2 t)}{4} + \frac{t}{2}

t=2x

= \frac{\sin (4 x)}{4} + x

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