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Popular >

integral of 3/(e^x)

Solution

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

Solution

- \frac{3}{e ^{x}} + C

Solution steps

\int \frac{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 \frac{1}{e ^{x}} d x

Apply u-substitution

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

= 3 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 3 (- \frac{1}{u})

Substitute back

u = e^{x}

= 3 (- \frac{1}{e ^{x}})

Simplify

3 (- \frac{1}{e ^{x}}) : - \frac{3}{e ^{x}}

= - \frac{3}{e ^{x}}

Add a constant to the solution

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

Popular Examples

derivative of x^2e^{4x}

\frac{d}{d x} (x^{2} e^{4 x})

integral of 12x^3sqrt(x)

\int 12 x^{3} x d x

derivative of arctan(9x^4)derivative of

arctan (9 x^{4})

y^{^{'}} - y - e^{3 x} = 0

tangent of f(x)=9x^2-2x tangent of

f (x) = 9 x^{2} - 2 x

Frequently Asked Questions (FAQ)

What is the integral of 3/(e^x) ?
The integral of 3/(e^x) is -3/(e^x)+C