What is the integral of x^2*e^{x^3+4} ?

The integral of x^2*e^{x^3+4} is 1/3 e^{x^3+4}+C

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integral of x^2*e^{x^3+4}

\int x^{2} \cdot e^{x^{3} + 4} d x

\frac{1}{3} e^{x^{3} + 4} + C

Solution steps

\int x^{2} e^{x^{3} + 4} d x

Apply u-substitution

: \int \frac{e ^{u}}{3} d u

= \int \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 e^{u} d u

Use the common integral:

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

= \frac{1}{3} e^{u}

Substitute back

u = x^{3} + 4

= \frac{1}{3} e^{x^{3} + 4}

Add a constant to the solution

= \frac{1}{3} e^{x^{3} + 4} + C

\frac{d}{d x} (r (θ, x) cos (θ))

y = 4 arcsin (5) x^{5}

(1 + x)^{- 1}

y = - 3 x^{3} - 2 x^{2} - x + 3, (- 1, 5)

- \frac{1}{x ^{2}}

What is the integral of x^2*e^{x^3+4} ?
The integral of x^2*e^{x^3+4} is 1/3 e^{x^3+4}+C