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

The integral of e^{x^2}2x^3 is e^{x^2}x^2-e^{x^2}+C

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integral of e^{x^2}2x^3

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

e^{x^{2}} x^{2} - e^{x^{2}} + C

Solution steps

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

Take the constant out:

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

= 2 \cdot \int e^{x^{2}} x^{3} d x

Apply u-substitution

: \int \frac{e ^{u} u}{2} d u

= 2 \cdot \int \frac{e ^{u} u}{2} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= 2 \cdot \frac{1}{2} (e^{u} u - \int e^{u} d u)

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

= 2 \cdot \frac{1}{2} (e^{u} u - e^{u})

Substitute back

u = x^{2}

= 2 \cdot \frac{1}{2} (e^{x^{2}} x^{2} - e^{x^{2}})

Simplify

2 \cdot \frac{1}{2} (e^{x^{2}} x^{2} - e^{x^{2}}) : e^{x^{2}} x^{2} - e^{x^{2}}

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

Add a constant to the solution

= e^{x^{2}} x^{2} - e^{x^{2}} + C

x \to \infty lim (- 5)

f (t) = arcsin (8 t)

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

\int e^{\frac{1}{2 x}} d x

\int \frac{1}{576 + x ^{2}} d x

What is the integral of e^{x^2}2x^3 ?
The integral of e^{x^2}2x^3 is e^{x^2}x^2-e^{x^2}+C