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Popular >

integral of e^{-3x^2-1}x

Solution

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

Solution

- \frac{1}{6} e^{- 3 x^{2} - 1} + C

Solution steps

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

Apply u-substitution

: \int - \frac{e ^{u}}{6} d u

= \int - \frac{e ^{u}}{6} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{6} e^{u}

Substitute back

u = - 3 x^{2} - 1

= - \frac{1}{6} e^{- 3 x^{2} - 1}

Add a constant to the solution

= - \frac{1}{6} e^{- 3 x^{2} - 1} + C

Popular Examples

integral of (3x^6+4x^2+12)/(x^4)

\int \frac{3 x ^{6} + 4 x ^{2} + 12}{x ^{4}} d x

integral of (8x^3-3x^2+4)

\int (8 x^{3} - 3 x^{2} + 4) d x

integral of 3^{(2x+4)}

\int 3^{(2 x + 4)} d x

integral of x^4(1-x^2)^{3/2}

\int x^{4} (1 - x^{2})^{\frac{3}{2}} d x

integral of (x^2)/(sqrt(4x^2+9))

\int \frac{x ^{2}}{4 x ^{2} + 9} d x

Frequently Asked Questions (FAQ)

What is the integral of e^{-3x^2-1}x ?
The integral of e^{-3x^2-1}x is -1/6 e^{-3x^2-1}+C