What is the integral from 1 to e^x of x/y ?

The integral from 1 to e^x of x/y is x^2

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integral from 1 to e^x of x/y

\int_{1}^{e^{x}} \frac{x}{y} d y

x^{2}

Solution steps

\int_{1}^{e^{x}} \frac{x}{y} d y

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= x [ln ∣ y ∣]_{1}^{e^{x}}

Compute the boundaries:

x

= xx

Simplify

= x^{2}

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

\int_{1}^{x} 2 - x d x

\int_{2}^{6} (x + 3)^{2} d x

\int_{2 t}^{3 t} \frac{sin ( x )}{2 x} d x

\int_{0}^{1} 2 y^{3} d y

What is the integral from 1 to e^x of x/y ?
The integral from 1 to e^x of x/y is x^2