What is the integral from 0 to 2 of 3/(x+4) ?

The integral from 0 to 2 of 3/(x+4) is 3ln(3/2)

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integral from 0 to 2 of 3/(x+4)

\int_{0}^{2} \frac{3}{x + 4} d x

3 ln (\frac{3}{2})

Decimal

1.21639 \dots

Solution steps

\int_{0}^{2} \frac{3}{x + 4} d x

Take the constant out:

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

= 3 \cdot \int_{0}^{2} \frac{1}{x + 4} d x

Apply u-substitution

: \int_{4}^{6} \frac{1}{u} d u

= 3 \cdot \int_{4}^{6} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 [ln ∣ u ∣]_{4}^{6}

Compute the boundaries:

ln (6) - 2 ln (2)

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

Simplify

= 3 ln (\frac{3}{2})

\int_{0}^{y} x e^{- y} d x

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\int_{0}^{\frac{π}{4}} (2 cos (x) + 1) d x

\int_{0}^{1} x (\frac{3}{2} x^{2} + \frac{1}{2}) d x

What is the integral from 0 to 2 of 3/(x+4) ?
The integral from 0 to 2 of 3/(x+4) is 3ln(3/2)