What is the integral of 5e^{(5s+sqrt(8))} ?

The integral of 5e^{(5s+sqrt(8))} is e^{2sqrt(2)+5s}+C

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integral of 5e^{(5s+sqrt(8))}

\int 5 e^{(5 s + 8)} d s

e^{22 + 5 s} + C

Solution steps

\int 5 e^{5 s + 8} d s

Take the constant out:

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

= 5 \cdot \int e^{5 s + 8} d s

e^{5 s + 8} = e^{8} e^{5 s}

= 5 \cdot \int e^{8} e^{5 s} d s

Take the constant out:

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

= 5 e^{8} \cdot \int e^{5 s} d s

8 = 22

= 5 e^{22} \cdot \int e^{5 s} d s

Apply u-substitution

: \int e^{u} \frac{1}{5} d u

= 5 e^{22} \cdot \int e^{u} \frac{1}{5} d u

Take the constant out:

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

= 5 e^{22} \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

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

= 5 e^{22} \frac{1}{5} e^{u}

Substitute back

u = 5 s

= 5 e^{22} \frac{1}{5} e^{5 s}

Simplify

5 e^{22} \frac{1}{5} e^{5 s} : e^{22 + 5 s}

= e^{22 + 5 s}

Add a constant to the solution

= e^{22 + 5 s} + C

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What is the integral of 5e^{(5s+sqrt(8))} ?
The integral of 5e^{(5s+sqrt(8))} is e^{2sqrt(2)+5s}+C