What is the integral of (e^{7sqrt(t)})/(sqrt(t)) ?

The integral of (e^{7sqrt(t)})/(sqrt(t)) is 2/7 e^{7sqrt(t)}+C

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integral of (e^{7sqrt(t)})/(sqrt(t))

\int \frac{e ^{7 t}}{t} d t

\frac{2}{7} e^{7 t} + C

Solution steps

\int \frac{e ^{7 t}}{t} d t

Apply u-substitution

: \int \frac{2 e ^{u}}{7} d u

= \int \frac{2 e ^{u}}{7} d u

Take the constant out:

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

= \frac{2}{7} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{2}{7} e^{u}

Substitute back

u = 7 t

= \frac{2}{7} e^{7 t}

Add a constant to the solution

= \frac{2}{7} e^{7 t} + C

x \to 5 lim (\frac{3 x ^{2} - 13 x - 10}{2 x ^{2} - 7 x - 15})

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

\int 9 x e^{17 x} d x

\int cot^{3} (2 x) d x

(x^{2} + 4)^{7}

What is the integral of (e^{7sqrt(t)})/(sqrt(t)) ?
The integral of (e^{7sqrt(t)})/(sqrt(t)) is 2/7 e^{7sqrt(t)}+C