What is the integral of e^{100t}*60 ?

The integral of e^{100t}*60 is 3/5 e^{100t}+C

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integral of e^{100t}*60

\int e^{100 t} \cdot 60 d t

\frac{3}{5} e^{100 t} + C

Solution steps

\int e^{100 t} \cdot 60 d t

Take the constant out:

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

= 60 \cdot \int e^{100 t} d t

Apply u-substitution

: \int e^{u} \frac{1}{100} d u

= 60 \cdot \int e^{u} \frac{1}{100} d u

Take the constant out:

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

= 60 \cdot \frac{1}{100} \cdot \int e^{u} d u

Use the common integral:

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

= 60 \cdot \frac{1}{100} e^{u}

Substitute back

u = 100 t

= 60 \cdot \frac{1}{100} e^{100 t}

Simplify

60 \cdot \frac{1}{100} e^{100 t} : \frac{3}{5} e^{100 t}

= \frac{3}{5} e^{100 t}

Add a constant to the solution

= \frac{3}{5} e^{100 t} + C

x \to 3 lim (\frac{4}{x - 3})

f (x) = 3 (x - 2)^{2}

x y^{^{'}} + y = x^{4} y^{4}, y (1) = \frac{1}{2}

y = e^{- m x}

3 sin (2 x)

What is the integral of e^{100t}*60 ?
The integral of e^{100t}*60 is 3/5 e^{100t}+C