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

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

Popular >

integral of 2e^{x^2}x

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

e^{x^{2}} + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

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

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

Substitute back

u = x^{2}

= 2 \cdot \frac{1}{2} e^{x^{2}}

Simplify

2 \cdot \frac{1}{2} e^{x^{2}} : e^{x^{2}}

= e^{x^{2}}

Add a constant to the solution

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

\int (- x^{5} + 9) d x

\int cos^{2} (π x) sin (π x) d x

\int e^{t^{4}} d t

\int x e^{\frac{x}{a}} d x

\int \frac{( x ^{3} - x ^{2} - 12 )}{x} d x