What is the integral from ln(9) to ln(25) of e^{x/2} ?

The integral from ln(9) to ln(25) of e^{x/2} is 4

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integral from ln(9) to ln(25) of e^{x/2}

\int_{l n (9)}^{l n (25)} e^{\frac{x}{2}} d x

4

Solution steps

\int_{l n (9)}^{l n (25)} e^{\frac{x}{2}} d x

Apply u-substitution

: \int_{l n (3)}^{l n (5)} e^{u} \cdot 2 d u

= \int_{l n (3)}^{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 (3)}^{l n (5)} e^{u} d u

Use the common integral:

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

= 2 [e^{u}]_{l n (3)}^{l n (5)}

Compute the boundaries:

2

= 2 \cdot 2

Simplify

= 4

\frac{d}{d x} (144)

5 - x^{2}, sin (x), - 2, 2

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\int_{1}^{3} \frac{2.25}{x ^{3}} d x

\frac{- 3 x ^{6} - x ^{5} + 3 x ^{4}}{x ^{2}}

What is the integral from ln(9) to ln(25) of e^{x/2} ?
The integral from ln(9) to ln(25) of e^{x/2} is 4