What is the integral from 2 to 12 of 1/(27t+36) ?

The integral from 2 to 12 of 1/(27t+36) is 2/27 ln(2)

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integral from 2 to 12 of 1/(27t+36)

\int_{2}^{12} \frac{1}{27 t + 36} d t

\frac{2}{27} ln (2)

Decimal Notation

0.05134 \dots

Solution steps

\int_{2}^{12} \frac{1}{27 t + 36} d t

Apply u-substitution

: \int_{90}^{360} \frac{1}{27 u} d u

= \int_{90}^{360} \frac{1}{27 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{27} \cdot \int_{90}^{360} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{27} [ln ∣ u ∣]_{90}^{360}

Compute the boundaries:

ln (360) - ln (90)

= \frac{1}{27} (ln (360) - ln (90))

Simplify

= \frac{2}{27} ln (2)

\int \frac{x + 2}{( x ^{2} + x + 1 )} d x

x^{2} - 3 x - 4

y = 7 x^{3}

\frac{\partial}{\partial x} (ln (x^{2} + y^{2} + 4))

\int \frac{x ^{2}}{1 - x ^{6}} d x

What is the integral from 2 to 12 of 1/(27t+36) ?
The integral from 2 to 12 of 1/(27t+36) is 2/27 ln(2)