How do you integrate #int ln(e^(2x-1))dx#?

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Answer 1 · 2018-06-26T08:59:58

# x^2 - x +c #

Use knowledge of logarithms

# log_a a^f(x) -= f(x) ln_a a -= f(x) #

Hence #ln e^f(x) -= f(x) #

#=> int ln (e^(2x-1) ) dx = int (2x-1) dx#

Use the reverse power rule:

# = x^2 -x + c #