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Popular >

integral of sqrt(9x)

Solution

\int 9 x d x

Solution

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

Solution steps

\int 9 x d x

Simplify

9 x : 3 x

= \int 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 d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral from 0 to 20 of 2^{t/(10)}

\int_{0}^{20} 2^{\frac{t}{10}} d t

(\partial)/(\partial x)(-2+e^{-x}cos(y))

\frac{\partial}{\partial x} (- 2 + e^{- x} cos (y))

derivative of (10)/(\sqrt[5]{x)}derivative of

\frac{10}{5 x}

derivative of ((x-1))/(x+1)derivative of

\frac{( x - 1 )}{x + 1}

derivative of f(x)=(x)^3e^{(3x)}derivative of

f (x) = (x)^{3} e^{(3 x)}

Frequently Asked Questions (FAQ)

What is the integral of sqrt(9x) ?
The integral of sqrt(9x) is 2x^{3/2}+C