What is the integral from 1 to 5 of 4x^2ln(x) ?

The integral from 1 to 5 of 4x^2ln(x) is 4(-124/9+125/3 ln(5))

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integral from 1 to 5 of 4x^2ln(x)

\int_{1}^{5} 4 x^{2} ln (x) d x

4 (- \frac{124}{9} + \frac{125}{3} ln (5))

Decimal Notation

213.12854 \dots

Solution steps

\int_{1}^{5} 4 x^{2} ln (x) d x

Take the constant out:

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

= 4 \cdot \int_{1}^{5} x^{2} ln (x) d x

Apply Integration By Parts

: [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{1}^{5}

= 4 [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{1}^{5}

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

= 4 [\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}]_{1}^{5}

Compute the boundaries:

- \frac{124}{9} + \frac{125}{3} ln (5)

= 4 (- \frac{124}{9} + \frac{125}{3} ln (5))

f^{^{'}} (x) = 2 sin (6 x), f (\frac{π}{6}) = - \frac{5}{2}

x \to 1 lim (sin (5 p i x))

x \to 1 + lim (\frac{x ^{2} + 1}{x - 1})

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

8 x^{3} + 2 x + 7 x^{\frac{1}{3}}

What is the integral from 1 to 5 of 4x^2ln(x) ?
The integral from 1 to 5 of 4x^2ln(x) is 4(-124/9+125/3 ln(5))