What is the integral of e^{(a-s)x} ?

The integral of e^{(a-s)x} is 1/(a-s)e^{(a-s)x}+C

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integral of e^{(a-s)x}

\int e^{(a - s) x} d x

\frac{1}{a - s} e^{(a - s) x} + C

Solution steps

\int e^{(a - s) x} d x

Apply u-substitution

: \int \frac{e ^{u}}{a - s} d u

= \int \frac{e ^{u}}{a - s} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{a - s} e^{u}

Substitute back

u = (a - s) x

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

Add a constant to the solution

= \frac{1}{a - s} e^{(a - s) x} + C

\int tan^{3} (8 x) sec (8 x) d x

\int \frac{10}{x ^{4}} d x

\int \frac{6 x ^{2} + 2 x - 1}{3 x ^{2}} d x

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

f (x) = x^{2} e^{4 x}

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