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

The integral from 0 to 3 of 3/(x+4) is 3(ln(7)-2ln(2))

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

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

3 (ln (7) - 2 ln (2))

Decimal Notation

1.67884 \dots

Solution steps

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

Apply u-substitution

: \int_{4}^{7} \frac{1}{u} d u

= 3 \cdot \int_{4}^{7} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 [ln ∣ u ∣]_{4}^{7}

Compute the boundaries:

ln (7) - 2 ln (2)

= 3 (ln (7) - 2 ln (2))

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

\int_{0}^{5} e^{- x^{2}} d x

\int_{- 3}^{1} (e^{x + 3}) d x

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

\int_{- 1}^{2} 4 t^{2} + 5 d t

What is the integral from 0 to 3 of 3/(x+4) ?
The integral from 0 to 3 of 3/(x+4) is 3(ln(7)-2ln(2))