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Popular >

integral of 3x^{1/2}

Solution

\int 3 x^{\frac{1}{2}} d x

Solution

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

Solution steps

\int 3 x^{\frac{1}{2}} d x

Take the constant out:

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

= 3 \cdot \int x^{\frac{1}{2}} 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

tangent of y=x^3+3x^2+2 tangent of

y = x^{3} + 3 x^{2} + 2

derivative of (e^{-t}/((x^2+y(t,x)^2)^2))

\frac{d}{d x} \frac{e ^{- t}}{( x ^{2} + y ( t , x ) ^{2} ) ^{2}}

integral of (sec^2(x))/(tan^4(x))

\int \frac{sec ^{2} ( x )}{tan ^{4} ( x )} d x

y^{^{'}} + x y = x y^{2}

integral from a to b of 1/(x^3)

\int_{a}^{b} \frac{1}{x ^{3}} d x

Frequently Asked Questions (FAQ)

What is the integral of 3x^{1/2} ?
The integral of 3x^{1/2} is 2x^{3/2}+C