What is the integral of (3^{1+sqrt(x)}-5)/(sqrt(x)) ?

The integral of (3^{1+sqrt(x)}-5)/(sqrt(x)) is (6*3^{sqrt(x)})/(ln(3))-10sqrt(x)+C

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integral of (3^{1+sqrt(x)}-5)/(sqrt(x))

\int \frac{3 ^{1 + x} - 5}{x} d x

\frac{6 \cdot 3 ^{x}}{ln ( 3 )} - 10 x + C

Solution steps

\int \frac{3 ^{1 + x} - 5}{x} d x

3^{1 + x} = 3^{1} \cdot 3^{x}

= \int \frac{3 ^{1} \cdot 3 ^{x} - 5}{x} d x

Expand

\frac{3 ^{1} \cdot 3 ^{x} - 5}{x} : \frac{3 \cdot 3 ^{x}}{x} - \frac{5}{x}

= \int \frac{3 \cdot 3 ^{x}}{x} - \frac{5}{x} d x

Apply the Sum Rule:

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

= \int \frac{3 \cdot 3 ^{x}}{x} d x - \int \frac{5}{x} d x

\int \frac{3 \cdot 3 ^{x}}{x} d x = \frac{6 \cdot 3 ^{x}}{ln ( 3 )}

\int \frac{5}{x} d x = 10 x

= \frac{6 \cdot 3 ^{x}}{ln ( 3 )} - 10 x

Add a constant to the solution

= \frac{6 \cdot 3 ^{x}}{ln ( 3 )} - 10 x + C

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What is the integral of (3^{1+sqrt(x)}-5)/(sqrt(x)) ?
The integral of (3^{1+sqrt(x)}-5)/(sqrt(x)) is (6*3^{sqrt(x)})/(ln(3))-10sqrt(x)+C