Question

# Find the integral of the function tan(3ln(x))x

A
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B
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C
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D
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Solution

## The correct option is D We saw that ∫tanxdx=ln|secx|+c We have lnx and it’s derivative 1x in the function we want to integrate. So the substitution we make would be, 3 lnx = u. (If we substitute lnx = u, we would need one more substitution to account for 3 inside tan function(or more steps). ⇒3lnx=u⇒du=3xdx⇒1xdx=du3 So the integral ∫tan(3ln(x))xdx becomes ∫tan(u)du3 This will be equal to ln|sec(u)|3 Replacing u with 3 lnx, we get ln|sec(3lnx)|3 ⇒∫tan(3ln(x))xdx=ln|sec(3lnx)|3+c

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