What is the integral from 1 to 3 of x^2e^{x^3-1} ?

The integral from 1 to 3 of x^2e^{x^3-1} is (e^{26}-1)/3

Popular >

integral from 1 to 3 of x^2e^{x^3-1}

\int_{1}^{3} x^{2} e^{x^{3} - 1} d x

\frac{e ^{26} - 1}{3}

Decimal

65243203142.61283

Solution steps

\int_{1}^{3} x^{2} e^{x^{3} - 1} d x

Apply u-substitution

: \int_{0}^{26} \frac{e ^{u}}{3} d u

= \int_{0}^{26} \frac{e ^{u}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{0}^{26} e^{u} d u

Use the common integral:

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

= \frac{1}{3} [e^{u}]_{0}^{26}

Compute the boundaries:

e^{26} - 1

= \frac{1}{3} (e^{26} - 1)

Simplify

= \frac{e ^{26} - 1}{3}

\int 2 x sin (x^{2}) + \frac{1}{x ^{2}} sin (\frac{1}{x}) d x

y = \frac{7}{sin ( x ) + cos ( x )}, (0, 7)

\frac{d}{d x} (2^{3 x - 1})

y = \frac{x}{1 + x ^{2}}, (3, 0.3)

x \to 0 + lim (\frac{2}{x} - \frac{2}{∣ x ∣})

What is the integral from 1 to 3 of x^2e^{x^3-1} ?
The integral from 1 to 3 of x^2e^{x^3-1} is (e^{26}-1)/3