What is the integral of e^{R/L t} ?

The integral of e^{R/L t} is L/R e^{(Rt)/L}+C

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integral of e^{R/L t}

\int e^{\frac{R}{L} t} d t

\frac{L}{R} e^{\frac{Rt}{L}} + C

Solution steps

\int e^{\frac{R}{L} t} d t

\frac{R}{L} = R \frac{1}{L}

= \int e^{R \frac{1}{L} t} d t

Multiply

R \frac{1}{L} t : \frac{Rt}{L}

= \int e^{\frac{Rt}{L}} d t

Apply u-substitution

: \int \frac{L e ^{u}}{R} d u

= \int \frac{L e ^{u}}{R} d u

Take the constant out:

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

= \frac{L}{R} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{L}{R} e^{u}

Substitute back

u = \frac{Rt}{L}

= \frac{L}{R} e^{\frac{Rt}{L}}

Add a constant to the solution

= \frac{L}{R} e^{\frac{Rt}{L}} + C

f (x) = 4 x - 3 x + 7

\int \frac{1}{x ^{2} + 2 x + 101} d x

\int \frac{2}{2 - x ^{2}} d x

\frac{\partial}{\partial x} (f (x, y))

What is the integral of e^{R/L t} ?
The integral of e^{R/L t} is L/R e^{(Rt)/L}+C