What is the integral from x^3 to x of e^{y/x} ?

The integral from x^3 to x of e^{y/x} is x(e-e^{x^2})

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integral from x^3 to x of e^{y/x}

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

x (e - e^{x^{2}})

Solution steps

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

Apply u-substitution

: \int_{x^{2}}^{1} e^{u} x d u

= \int_{x^{2}}^{1} e^{u} x d u

Take the constant out:

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

= x \cdot \int_{x^{2}}^{1} e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= x [e^{u}]_{x^{2}}^{1}

Compute the boundaries:

e - e^{x^{2}}

= x (e - e^{x^{2}})

\int_{0}^{x} \frac{1}{( 1 - x ) ^{2.37}} d x

\int_{3}^{6} (2 x + 1)^{2} d x

\int_{0}^{2} e^{y} d y

\int_{0}^{1} (x^{4} + x^{6}) d x

\int_{2}^{3} (x - 2)^{2} d x

What is the integral from x^3 to x of e^{y/x} ?
The integral from x^3 to x of e^{y/x} is x(e-e^{x^2})