What is the integral from 1 to 2 of ln(3x) ?

The integral from 1 to 2 of ln(3x) is ln(12)-1

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integral from 1 to 2 of ln(3x)

\int_{1}^{2} ln (3 x) d x

ln (12) - 1

Decimal Notation

1.48490 \dots

Solution steps

\int_{1}^{2} ln (3 x) d x

Apply Integration By Parts

: [x ln (3 x) - \int 1 d x]_{1}^{2}

= [x ln (3 x) - \int 1 d x]_{1}^{2}

\int 1 d x = x

= [x ln (3 x) - x]_{1}^{2}

Compute the boundaries:

2 ln (6) - 1 - ln (3)

= 2 ln (6) - 1 - ln (3)

Simplify

= ln (12) - 1

\int \frac{sin ( 2 x )}{33 + cos ^{2} ( x )} d x

\frac{d}{d x} ((x^{2} + 3) \cdot x)

x^{2} + 36

x \to 1 + lim (x^{\frac{1}{( x - 1 )}})

\int cos^{9} (x) tan^{3} (x) d x

What is the integral from 1 to 2 of ln(3x) ?
The integral from 1 to 2 of ln(3x) is ln(12)-1