What is the integral of (e^{-1/(x^2)-3ln(x)}*1) ?

The integral of (e^{-1/(x^2)-3ln(x)}*1) is 1/2 e^{-1/(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 (e^{-1/(x^2)-3ln(x)}*1)

\int (e^{- \frac{1}{x ^{2}} - 3 l n (x)} \cdot 1) d x

\frac{1}{2} e^{- \frac{1}{x ^{2}}} + C

Solution steps

\int e^{- \frac{1}{x ^{2}} - 3 l n (x)} \cdot 1 d x

Simplify

e^{- \frac{1}{x ^{2}} - 3 l n (x)} \cdot 1 : \frac{e ^{- \frac{1}{x ^{2}}}}{x ^{3}}

= \int \frac{e ^{- \frac{1}{x ^{2}}}}{x ^{3}} d x

Apply u-substitution

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

= \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

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

Use the common integral:

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

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

Substitute back

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

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

Add a constant to the solution

= \frac{1}{2} e^{- \frac{1}{x ^{2}}} + C

\int \frac{( 3 x - 1 )}{x ^{2} + 9} d x

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

\frac{d}{d x} (sin (x) + csc (x))

\frac{x d y}{d x} = 2 x e^{x} - y + 6 x^{2}

y^{^{''}} + 2 y^{^{'}} + y = x^{2}

What is the integral of (e^{-1/(x^2)-3ln(x)}*1) ?
The integral of (e^{-1/(x^2)-3ln(x)}*1) is 1/2 e^{-1/(x^2)}+C