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Popular >

integral of 3sqrt(x)

Solution

\int 3 x d x

Solution

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

Solution steps

\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

Popular Examples

integral of sin^2(2x)cos^2(x)

\int sin^{2} (2 x) cos^{2} (x) d x

limit as x approaches 0 of (1-10x)^{1/x}

x \to 0 lim ((1 - 10 x)^{\frac{1}{x}})

limit as x approaches infinity+of x^{(3)}e^{(-x^{(2)})}

x \to \infty + lim (x^{(3)} e^{(- x^{(2)})})

(dy)/(dx)y=(2cos(x))/(1+sin(x))

\frac{d y}{d x} y = \frac{2 cos ( x )}{1 + sin ( x )}

derivative of f(x)=(11x^2-22x+22)e^x derivative of

f (x) = (11 x^{2} - 22 x + 22) e^{x}

Frequently Asked Questions (FAQ)

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