What is the integral from e to e^3 of (15)/y ?

The integral from e to e^3 of (15)/y is 30

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integral from e to e^3 of (15)/y

\int_{e}^{e^{3}} \frac{15}{y} d y

30

Solution steps

\int_{e}^{e^{3}} \frac{15}{y} d y

Take the constant out:

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

= 15 \cdot \int_{e}^{e^{3}} \frac{1}{y} d y

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= 15 [ln ∣ y ∣]_{e}^{e^{3}}

Compute the boundaries:

2

= 15 \cdot 2

Simplify

= 30

\int x^{2} cos^{2} (x) d x

y^{^{''}} + 8 y^{^{'}} - 9 y = 0, y (1) = 2, y^{^{'}} (1) = 0

\frac{d y}{d x} = \frac{e ^{2 x}}{4 y ^{3}}

\frac{d}{d x} (ln (cos^{2} (x) + 5 x^{3}))

y^{^{''}} = - k^{2} y

What is the integral from e to e^3 of (15)/y ?
The integral from e to e^3 of (15)/y is 30