What is the integral of 3/4 x^{1/2} ?

The integral of 3/4 x^{1/2} is 1/2 x^{3/2}+C

Popular >

integral of 3/4 x^{1/2}

\int \frac{3}{4} x^{\frac{1}{2}} d x

\frac{1}{2} x^{\frac{3}{2}} + C

Solution steps

\int \frac{3}{4} x^{\frac{1}{2}} d x

Take the constant out:

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

= \frac{3}{4} \cdot \int x^{\frac{1}{2}} d x

Apply the Power Rule

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

= \frac{3}{4} \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

\frac{3}{4} \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{1}{2} x^{\frac{3}{2}}

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

Add a constant to the solution

= \frac{1}{2} x^{\frac{3}{2}} + C

\int_{1}^{8} (\frac{x ^{- \frac{1}{2}}}{1 + x ^{\frac{1}{2}}}) d x

\int \frac{5 r ^{2}}{r + 5} d r

\int e^{x - y} d x

\int t sec^{2} (8 t) d t

\frac{d ^{2} y}{d t ^{2}} + 7 \frac{d y}{d t} + 12 y = 0

What is the integral of 3/4 x^{1/2} ?
The integral of 3/4 x^{1/2} is 1/2 x^{3/2}+C