What is the integral from 1 to 5 of 1/(1+2x) ?

The integral from 1 to 5 of 1/(1+2x) is 1/2 (ln(11)-ln(3))

Popular >

integral from 1 to 5 of 1/(1+2x)

\int_{1}^{5} \frac{1}{1 + 2 x} d x

\frac{1}{2} (ln (11) - ln (3))

Decimal Notation

0.64964 \dots

Solution steps

\int_{1}^{5} \frac{1}{1 + 2 x} d x

Apply u-substitution

: \int_{3}^{11} \frac{1}{2 u} d u

= \int_{3}^{11} \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{3}^{11} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{3}^{11}

Compute the boundaries:

ln (11) - ln (3)

= \frac{1}{2} (ln (11) - ln (3))

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

∣ x - 2 ∣, 0 = x - 3 y + 6

\int_{2}^{3} \frac{40}{3 - x} d x

\frac{d}{d x} (\frac{cos ( x )}{1 + a sin ( x )})

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

What is the integral from 1 to 5 of 1/(1+2x) ?
The integral from 1 to 5 of 1/(1+2x) is 1/2 (ln(11)-ln(3))