What is the integral from 0 to 1 of 5ln(x) ?

The integral from 0 to 1 of 5ln(x) is -5

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integral from 0 to 1 of 5ln(x)

\int_{0}^{1} 5 ln (x) d x

- 5

Solution steps

\int_{0}^{1} 5 ln (x) d x

Take the constant out:

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

= 5 \cdot \int_{0}^{1} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{0}^{1}

= 5 [x ln (x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 5 [x ln (x) - x]_{0}^{1}

Compute the boundaries:

- 1

= 5 (- 1)

Simplify

= - 5

f (x) = x \cdot e^{- x + 1}

\int_{1}^{e} \frac{1}{x ( x ^{2} + 1 )} d x

\frac{d y}{d x} = y + x y^{3}

y = 2 csc (4 x^{4} - 2 x + 5)

x^{^{''}} + 9 x = 0

What is the integral from 0 to 1 of 5ln(x) ?
The integral from 0 to 1 of 5ln(x) is -5