What is the integral of e^{t/(50)} ?

The integral of e^{t/(50)} is 50e^{t/(50)}+C

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integral of e^{t/(50)}

\int e^{\frac{t}{50}} d t

50 e^{\frac{t}{50}} + C

Solution steps

\int e^{\frac{t}{50}} d t

Apply u-substitution

: \int e^{u} \cdot 50 d u

= \int e^{u} \cdot 50 d u

Take the constant out:

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

= 50 \cdot \int e^{u} d u

Use the common integral:

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

= 50 e^{u}

Substitute back

u = \frac{t}{50}

= 50 e^{\frac{t}{50}}

Add a constant to the solution

= 50 e^{\frac{t}{50}} + C

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

\frac{d}{d x} (x (ln (x))^{2})

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

h \to 0 lim (\frac{( x + h ) ^{- 5} - x ^{- 5}}{h})

\int \frac{x}{x + 1} d x

What is the integral of e^{t/(50)} ?
The integral of e^{t/(50)} is 50e^{t/(50)}+C