What is the integral from 0.5 to 1 of (ln(x))/(4x) ?

The integral from 0.5 to 1 of (ln(x))/(4x) is -0.06005…

Popular >

integral from 0.5 to 1 of (ln(x))/(4x)

\int_{0.5}^{1} \frac{ln ( x )}{4 x} d x

- 0.06005 \dots

Solution steps

\int_{0.5}^{1} \frac{ln ( x )}{4 x} d x

Take the constant out:

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

= \frac{1}{4} \cdot \int_{0.5}^{1} \frac{ln ( x )}{x} d x

Apply u-substitution

: \int_{- 0.69314 \dots}^{0} u d u

= \frac{1}{4} \cdot \int_{- 0.69314 \dots}^{0} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{- 0.69314 \dots}^{0}

= \frac{1}{4} [\frac{u ^{2}}{2}]_{- 0.69314 \dots}^{0}

Simplify

= 0.25 [0.5 u^{2}]_{- 0.69314 \dots}^{0}

Compute the boundaries:

- 0.24022 \dots

= 0.25 (- 0.24022 \dots)

Simplify

= - 0.06005 \dots

\int_{1}^{x} x^{4} + 1 d x

\int_{- 2}^{2} 4 x y^{3} d y

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

\int_{0}^{1} 5 x^{2} e^{x^{3}} d x

\int_{2}^{5} \frac{1}{( x - 2 ) ^{- 1}} d x

What is the integral from 0.5 to 1 of (ln(x))/(4x) ?
The integral from 0.5 to 1 of (ln(x))/(4x) is -0.06005…