What is the integral from 1 to 16 of x^{1/2}ln(x) ?

The integral from 1 to 16 of x^{1/2}ln(x) is -28+512/3 ln(2)

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integral from 1 to 16 of x^{1/2}ln(x)

\int_{1}^{16} x^{\frac{1}{2}} ln (x) d x

- 28 + \frac{512}{3} ln (2)

Decimal

90.29711 \dots

Solution steps

\int_{1}^{16} x^{\frac{1}{2}} ln (x) d x

Apply Integration By Parts

: [\frac{2}{3} x^{\frac{3}{2}} ln (x) - \int \frac{2}{3} x^{\frac{1}{2}} d x]_{1}^{16}

= [\frac{2}{3} x^{\frac{3}{2}} ln (x) - \int \frac{2}{3} x^{\frac{1}{2}} d x]_{1}^{16}

\int \frac{2}{3} x^{\frac{1}{2}} d x = \frac{4}{9} x^{\frac{3}{2}}

= [\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}}]_{1}^{16}

Compute the boundaries:

- 28 + \frac{512}{3} ln (2)

= - 28 + \frac{512}{3} ln (2)

f (x) = x^{2} + x - 6

\frac{d}{d x} (5 \cdot sin (x))

\frac{d y}{d t} = t^{2} - 2

\int e^{l n (x)} x d x

f (x) = 3 x^{2} + 5 x + 1

What is the integral from 1 to 16 of x^{1/2}ln(x) ?
The integral from 1 to 16 of x^{1/2}ln(x) is -28+512/3 ln(2)