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Popular >

integral of-3e^{-x}

Solution

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

Solution

3 e^{- x} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int - e^{u} d u

= - 3 \cdot \int - e^{u} d u

Take the constant out:

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

= - 3 (- \int e^{u} d u)

Use the common integral:

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

= - 3 (- e^{u})

Substitute back

u = - x

= - 3 (- e^{- x})

Simplify

= 3 e^{- x}

Add a constant to the solution

= 3 e^{- x} + C

Popular Examples

integral of (x^2-4)^4(2x)

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

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

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

integral of 9sin^{-3/2}(x)cos^3(x)

\int 9 sin^{- \frac{3}{2}} (x) cos^{3} (x) d x

limit as x approaches 1 of x-8

x \to 1 lim (x - 8)

derivative of (x^3/(x^2+1))

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

Frequently Asked Questions (FAQ)

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