What is the integral of 2e^{x^2+ln(x)} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2e^{x^2+ln(x)}

\int 2 e^{x^{2} + l n (x)} d x

e^{x^{2}} + C

Solution steps

\int 2 e^{x^{2} + l n (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} + l n (x)} d x

Simplify

e^{x^{2} + l n (x)} : e^{x^{2}} 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 \frac{a x ^{2} + x}{3 x + 1} d x

\int \frac{4}{1 + sin ( x ) + cos ( x )} d x

\int - x ln (9 + x^{2}) d x

What is the integral of 2e^{x^2+ln(x)} ?
The integral of 2e^{x^2+ln(x)} is e^{x^2}+C