What is the integral of ((e^{sqrt(x)}-3))/(sqrt(x)) ?

The integral of ((e^{sqrt(x)}-3))/(sqrt(x)) is 2(e^{sqrt(x)}-3sqrt(x))+C

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integral of ((e^{sqrt(x)}-3))/(sqrt(x))

\int \frac{( e ^{x} - 3 )}{x} d x

2 (e^{x} - 3 x) + C

Solution steps

\int \frac{e ^{x} - 3}{x} d x

Apply u-substitution

: \int 2 (e^{u} - 3) d u

= \int 2 (e^{u} - 3) d u

Take the constant out:

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

= 2 \cdot \int e^{u} - 3 d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int e^{u} d u - \int 3 d u)

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

\int 3 d u = 3 u

= 2 (e^{u} - 3 u)

Substitute back

u = x

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

Add a constant to the solution

= 2 (e^{x} - 3 x) + C

\int cos (n t) d t

\frac{d}{d x} (x^{3} (x - 4))

91 - 90 e^{- 0.2 t}

\frac{6}{s} + 16 \cdot \frac{1}{s ^{2} + 16}

f (x) = \frac{2}{4 - x}, at x = - 1

What is the integral of ((e^{sqrt(x)}-3))/(sqrt(x)) ?
The integral of ((e^{sqrt(x)}-3))/(sqrt(x)) is 2(e^{sqrt(x)}-3sqrt(x))+C