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

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

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integral of 3^{sqrt(x)}

\int 3^{x} d x

2 (\frac{3 ^{x} x}{ln ( 3 )} - \frac{3 ^{x}}{ln ^{2} ( 3 )}) + C

Solution steps

\int 3^{x} d x

Apply u-substitution

: \int 3^{u} \cdot 2 u d u

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

Take the constant out:

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

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

Apply Integration By Parts

: \frac{3 ^{u} u}{ln ( 3 )} - \int \frac{3 ^{u}}{ln ( 3 )} d u

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

\int \frac{3 ^{u}}{ln ( 3 )} d u = \frac{3 ^{u}}{ln ^{2} ( 3 )}

= 2 (\frac{3 ^{u} u}{ln ( 3 )} - \frac{3 ^{u}}{ln ^{2} ( 3 )})

Substitute back

u = x

= 2 (\frac{3 ^{x} x}{ln ( 3 )} - \frac{3 ^{x}}{ln ^{2} ( 3 )})

Add a constant to the solution

= 2 (\frac{3 ^{x} x}{ln ( 3 )} - \frac{3 ^{x}}{ln ^{2} ( 3 )}) + C

2 + 3 + cos^{2} (x)

\int \frac{2}{x ^{4}} d x

\int 4 y^{3} e^{y} d y

t e^{4 t}

\frac{d}{d x} (a x sin (x) + b x cos (x))

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