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olya-2409 [2.1K]
3 years ago
14

Find integral∫cos³x dx) )?​

Mathematics
2 answers:
atroni [7]3 years ago
8 0

cos³(<em>x</em>) = cos(<em>x</em>) cos²(<em>x</em>)

… = cos(<em>x</em>) (1 - sin²(<em>x</em>))

Substitute <em>u</em> = sin(<em>x</em>) and d<em>u</em> = cos(<em>x</em>) d<em>x</em>. Then in the integral, you get

∫ cos³(<em>x</em>) d<em>x</em> = ∫ (1 - <em>u</em> ²) d<em>u</em>

… = <em>u</em> - 1/3 <em>u</em> ³ + <em>C</em>

… = sin(<em>x</em>) - 1/3 sin³(<em>x</em>) + <em>C</em>

son4ous [18]3 years ago
4 0

Answer:

sin(x)−1/3(sin3(x))+C

Step-by-step explanation:

use u substitution method to integrate

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