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Popular >

integral of (e^x)/(e^{-6x)}

Solution

\int \frac{e ^{x}}{e ^{- 6 x}} d x

Solution

\frac{1}{7} e^{7 x} + C

Solution steps

\int \frac{e ^{x}}{e ^{- 6 x}} d x

Simplify

\frac{e ^{x}}{e ^{- 6 x}} : e^{7 x}

= \int e^{7 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{7} d u

= \int e^{u} \frac{1}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{7} e^{u}

Substitute back

u = 7 x

= \frac{1}{7} e^{7 x}

Add a constant to the solution

= \frac{1}{7} e^{7 x} + C

Popular Examples

derivative of (5x/(9x^2+1))

\frac{d}{d x} (\frac{5 x}{9 x ^{2} + 1})

y^{^{'}} = y - k

(x^2-4)((dy)/(dx))+4y=(x+2)^2

(x^{2} - 4) (\frac{d y}{d x}) + 4 y = (x + 2)^{2}

slope of (-7,-7),(-3,6)slope

(- 7, - 7), (- 3, 6)

integral of (cos^4(x))/(sin^6(x))

\int \frac{cos ^{4} ( x )}{sin ^{6} ( x )} d x

Frequently Asked Questions (FAQ)

What is the integral of (e^x)/(e^{-6x)} ?
The integral of (e^x)/(e^{-6x)} is 1/7 e^{7x}+C