What is the integral of e^{1/50 x} ?

The integral of e^{1/50 x} is 50e^{1/50 x}+C

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integral of e^{1/50 x}

\int e^{\frac{1}{50} x} d x

50 e^{\frac{1}{50} x} + C

Solution steps

\int e^{\frac{1}{50} x} d x

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{1}{50} x

= 50 e^{\frac{1}{50} x}

Add a constant to the solution

= 50 e^{\frac{1}{50} x} + C

\frac{d y}{d x} = - 5 y x

\int_{0}^{4} 1 + x d x

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

\int_{1}^{3} (- x^{2} + 4 x - 3) d x

x \to (0) lim (\frac{ln ( x )}{x})

What is the integral of e^{1/50 x} ?
The integral of e^{1/50 x} is 50e^{1/50 x}+C