What is the integral of e^{x^3+1} ?

The integral of e^{x^3+1} is e(-(x\Gamma(1/3 ,-x^3))/(3\sqrt[3]{-x^3)})+C

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integral of e^{x^3+1}

\int e^{x^{3} + 1} d x

e (- \frac{x Γ ( \frac{1}{3} , - x ^{3} )}{3 3 - x ^{3}}) + C

Solution steps

\int e^{x^{3} + 1} d x

e^{x^{3} + 1} = e^{1} e^{x^{3}}

= \int e^{1} e^{x^{3}} d x

Take the constant out:

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

= e^{1} \cdot \int e^{x^{3}} d x

Simplify

= e \cdot \int e^{x^{3}} d x

Use the nonelementary integral:

\int e^{x^{a}} d x = - \frac{x Γ ( \frac{1}{a} , - x ^{a} )}{a a - x ^{a}}

= e (- \frac{x Γ ( \frac{1}{3} , - x ^{3} )}{3 3 - x ^{3}})

Add a constant to the solution

= e (- \frac{x Γ ( \frac{1}{3} , - x ^{3} )}{3 3 - x ^{3}}) + C

(1 + x^{2}) y^{^{'}} - 2 x y = 0

x \to 10 lim (\frac{x ^{3}}{3})

(- 3 cos (2 x) - sin (3 x) - 4)^{2}

x \to 2 lim (3 - x + 7)

\frac{d}{d z} (e^{2 z})

What is the integral of e^{x^3+1} ?
The integral of e^{x^3+1} is e(-(x\Gamma(1/3 ,-x^3))/(3\sqrt[3]{-x^3)})+C