What is the integral from ln(4) to ln(25) of e^{x/2} ?

The integral from ln(4) to ln(25) of e^{x/2} is 6

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integral from ln(4) to ln(25) of e^{x/2}

\int_{l n (4)}^{l n (25)} e^{\frac{x}{2}} d x

6

Solution steps

\int_{l n (4)}^{l n (25)} e^{\frac{x}{2}} d x

Apply u-substitution

: \int_{l n (2)}^{l n (5)} e^{u} \cdot 2 d u

= \int_{l n (2)}^{l n (5)} e^{u} \cdot 2 d u

Take the constant out:

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

= 2 \cdot \int_{l n (2)}^{l n (5)} e^{u} d u

Use the common integral:

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

= 2 [e^{u}]_{l n (2)}^{l n (5)}

Compute the boundaries:

3

= 2 \cdot 3

Simplify

= 6

x \to 0 lim (- \frac{5}{1 - 5 x})

\frac{d y}{d x} = \frac{1}{1 - x}, y (0) = 1

f (x) = \frac{x ^{2} + 2 x - 4}{( x + 1 ) ^{2}}

x^{3} - x^{2} + 1

\int x \cdot ln (\frac{1 - x}{1 + x}) d x

What is the integral from ln(4) to ln(25) of e^{x/2} ?
The integral from ln(4) to ln(25) of e^{x/2} is 6