Let u = ln(x) <==> du = 1/x dx. Then, the integral becomes:
∫ cos[ln(x)]/x dx
= ∫ cos[ln(x)] (1/x dx)
= ∫ cos(u) du <== Apply substitutions
= sin(u) + C
= sin[ln(x)] + C. <== ANSWER
I hope this helps!
â« cos( ln x) / x dx
Let ln x = u
1/x dx = du
â« cos( ln x) / x dx = â« cos( u) du
= sin (ln x) + C
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Let u = ln(x) <==> du = 1/x dx. Then, the integral becomes:
∫ cos[ln(x)]/x dx
= ∫ cos[ln(x)] (1/x dx)
= ∫ cos(u) du <== Apply substitutions
= sin(u) + C
= sin[ln(x)] + C. <== ANSWER
I hope this helps!
â« cos( ln x) / x dx
Let ln x = u
1/x dx = du
â« cos( ln x) / x dx = â« cos( u) du
= sin(u) + C
= sin (ln x) + C