What is the integral of ln(e^{6x-7}) ?

The integral of ln(e^{6x-7}) is 3x^2-7x+C

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integral of ln(e^{6x-7})

\int ln (e^{6 x - 7}) d x

3 x^{2} - 7 x + C

Solution steps

\int ln (e^{6 x - 7}) d x

Apply Integration By Parts

: x (6 x - 7) - \int 6 x d x

= x (6 x - 7) - \int 6 x d x

\int 6 x d x = 3 x^{2}

= x (6 x - 7) - 3 x^{2}

Simplify

x (6 x - 7) - 3 x^{2} : 3 x^{2} - 7 x

= 3 x^{2} - 7 x

Add a constant to the solution

= 3 x^{2} - 7 x + C

(2 - x)^{^{'}}

\frac{d}{d x} ((9 x^{2} - 18 x + 18) e^{- 6 x})

\frac{d}{d x} (\frac{x ^{2} + 4}{x + 5})

\int_{1}^{e^{4}} \frac{ln ^{2} ( x ^{2} )}{x} d x

\int_{- 1}^{2} x^{3} d x

What is the integral of ln(e^{6x-7}) ?
The integral of ln(e^{6x-7}) is 3x^2-7x+C