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Popular >

integral of 4/(e^x)

Solution

\int \frac{4}{e ^{x}} d x

Solution

- \frac{4}{e ^{x}} + C

Solution steps

\int \frac{4}{e ^{x}} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{e ^{x}} d x

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= 4 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 4 (- \frac{1}{u})

Substitute back

u = e^{x}

= 4 (- \frac{1}{e ^{x}})

Simplify

4 (- \frac{1}{e ^{x}}) : - \frac{4}{e ^{x}}

= - \frac{4}{e ^{x}}

Add a constant to the solution

= - \frac{4}{e ^{x}} + C

Popular Examples

integral of e^{-11x}

\int e^{- 11 x} d x

inverse oflaplace (s+1)/(s^2+s+10)inverse laplace

\frac{s + 1}{s ^{2} + s + 10}

derivative of (sin(x))/(2x)derivative of

\frac{sin ( x )}{2 x}

(dy)/(dx)=-4(y-5)

\frac{d y}{d x} = - 4 (y - 5)

derivative of (4x+7^2)

\frac{d}{d x} ((4 x + 7)^{2})

Frequently Asked Questions (FAQ)

What is the integral of 4/(e^x) ?
The integral of 4/(e^x) is -4/(e^x)+C