What is the integral of (e^{-3t})/t ?

The integral of (e^{-3t})/t is \Ei(-3t)+C

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integral of (e^{-3t})/t

\int \frac{e ^{- 3 t}}{t} d t

Ei (- 3 t) + C

Solution steps

\int \frac{e ^{- 3 t}}{t} d t

Apply u-substitution

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

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

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= Ei (u)

Substitute back

u = - 3 t

= Ei (- 3 t)

Add a constant to the solution

= Ei (- 3 t) + C

\frac{1}{3} (3 - 5 x)^{3}

y y^{^{'}} + 4 x = 0

x \to 2 lim (\frac{x ^{3} + 8}{x + 2})

\int x^{2 x} (ln (x) + 1) d x

\frac{d}{d t} (2 t^{2})