What is the integral from 0 to 5 of x/(x+10) ?

The integral from 0 to 5 of x/(x+10) is 5-10ln(3/2)

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integral from 0 to 5 of x/(x+10)

\int_{0}^{5} \frac{x}{x + 10} d x

5 - 10 ln (\frac{3}{2})

Decimal Notation

0.94534 \dots

Solution steps

\int_{0}^{5} \frac{x}{x + 10} d x

Apply u-substitution

: \int_{10}^{15} \frac{u - 10}{u} d u

= \int_{10}^{15} \frac{u - 10}{u} d u

Expand

\frac{u - 10}{u} : 1 - \frac{10}{u}

= \int_{10}^{15} 1 - \frac{10}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{10}^{15} 1 d u - \int_{10}^{15} \frac{10}{u} d u

\int_{10}^{15} 1 d u = 5

\int_{10}^{15} \frac{10}{u} d u = 10 ln (\frac{3}{2})

= 5 - 10 ln (\frac{3}{2})

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

\frac{( d ^{2} y )}{( d x ^{2} )}

y = (2 x^{3} + 7)^{2}

(t - 2) e^{t}

x \to 4 - lim (\frac{∣ 4 - x ∣}{x - 4})

What is the integral from 0 to 5 of x/(x+10) ?
The integral from 0 to 5 of x/(x+10) is 5-10ln(3/2)