What is the integral from 0 to 6 of (300)/(3Q+2) ?

The integral from 0 to 6 of (300)/(3Q+2) is 100ln(10)

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integral from 0 to 6 of (300)/(3Q+2)

\int_{0}^{6} \frac{300}{3 Q + 2} d Q

100 ln (10)

Decimal

230.25850 \dots

Solution steps

\int_{0}^{6} \frac{300}{3 Q + 2} d Q

Take the constant out:

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

= 300 \cdot \int_{0}^{6} \frac{1}{3 Q + 2} d Q

Apply u-substitution

: \int_{2}^{20} \frac{1}{3 u} d u

= 300 \cdot \int_{2}^{20} \frac{1}{3 u} d u

Take the constant out:

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

= 300 \cdot \frac{1}{3} \cdot \int_{2}^{20} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 300 \cdot \frac{1}{3} [ln ∣ u ∣]_{2}^{20}

Simplify

300 \cdot \frac{1}{3} [ln ∣ u ∣]_{2}^{20} : 100 [ln ∣ u ∣]_{2}^{20}

= 100 [ln ∣ u ∣]_{2}^{20}

Compute the boundaries:

ln (20) - ln (2)

= 100 (ln (20) - ln (2))

Simplify

= 100 ln (10)

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What is the integral from 0 to 6 of (300)/(3Q+2) ?
The integral from 0 to 6 of (300)/(3Q+2) is 100ln(10)