What is the integral from 1 to 4 of 2sqrt(t)ln(t) ?

The integral from 1 to 4 of 2sqrt(t)ln(t) is 2(-28/9+32/3 ln(2))

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integral from 1 to 4 of 2sqrt(t)ln(t)

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

2 (- \frac{28}{9} + \frac{32}{3} ln (2))

Decimal Notation

8.56491 \dots

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

: [\frac{2}{3} t^{\frac{3}{2}} ln (t) - \int \frac{2}{3} t^{\frac{1}{2}} d t]_{1}^{4}

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

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

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

Compute the boundaries:

- \frac{28}{9} + \frac{32}{3} ln (2)

= 2 (- \frac{28}{9} + \frac{32}{3} ln (2))

\frac{\partial}{\partial x} (8 x^{6 y})

\frac{\partial}{\partial x} (20)

\frac{\partial}{\partial y} (\frac{1}{4} x^{2} + y^{2} - 1)

g (x) = x^{2} + sin (x)

f (x) = (x - 3 x^{4}) tan (x)

What is the integral from 1 to 4 of 2sqrt(t)ln(t) ?
The integral from 1 to 4 of 2sqrt(t)ln(t) is 2(-28/9+32/3 ln(2))