What is the integral of e^{3/200 t}3 ?

The integral of e^{3/200 t}3 is 200e^{3/200 t}+C

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integral of e^{3/200 t}3

\int e^{\frac{3}{200} t} 3 d t

200 e^{\frac{3}{200} t} + C

Solution steps

\int e^{\frac{3}{200} t} \cdot 3 d t

Take the constant out:

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

= 3 \cdot \int e^{\frac{3}{200} t} d t

Apply u-substitution

: \int e^{u} \frac{200}{3} d u

= 3 \cdot \int e^{u} \frac{200}{3} d u

Take the constant out:

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

= 3 \cdot \frac{200}{3} \cdot \int e^{u} d u

Use the common integral:

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

= 3 \cdot \frac{200}{3} e^{u}

Substitute back

u = \frac{3}{200} t

= 3 \cdot \frac{200}{3} e^{\frac{3}{200} t}

Simplify

3 \cdot \frac{200}{3} e^{\frac{3}{200} t} : 200 e^{\frac{3}{200} t}

= 200 e^{\frac{3}{200} t}

Add a constant to the solution

= 200 e^{\frac{3}{200} t} + C

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What is the integral of e^{3/200 t}3 ?
The integral of e^{3/200 t}3 is 200e^{3/200 t}+C