What is the integral of xsqrt(3x) ?

The integral of xsqrt(3x) is sqrt(3) 2/5 x^{5/2}+C

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integral of xsqrt(3x)

\int x 3 x d x

3 \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

\int x 3 x d x

Apply exponent rule:

(a \cdot b)^{n} = a^{n} \cdot b^{n}

3 x = 3 x

= \int x 3 x d x

Take the constant out:

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

= 3 \cdot \int x x d x

Simplify

x x : x^{\frac{3}{2}}

= 3 \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

: \frac{2}{5} x^{\frac{5}{2}}

= 3 \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= 3 \frac{2}{5} x^{\frac{5}{2}} + C

f (x) = (x^{2} \cdot 3^{x})^{7}

\int (x^{n} n (x)) d x

t y^{^{'}} + 2 y = 4 t^{2}, y (1) = 2

\frac{ln ( 2 x + 5 )}{ln ( 3 )}

\int e^{z} cos (x) d x

What is the integral of xsqrt(3x) ?
The integral of xsqrt(3x) is sqrt(3) 2/5 x^{5/2}+C