What is the integral of (3x^2-5x^{3/2}+6sqrt(x)) ?

The integral of (3x^2-5x^{3/2}+6sqrt(x)) is x^3-2x^{5/2}+4x^{3/2}+C

Popular >

integral of (3x^2-5x^{3/2}+6sqrt(x))

\int (3 x^{2} - 5 x^{\frac{3}{2}} + 6 x) d x

x^{3} - 2 x^{\frac{5}{2}} + 4 x^{\frac{3}{2}} + C

Solution steps

\int 3 x^{2} - 5 x^{\frac{3}{2}} + 6 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 x^{2} d x - \int 5 x^{\frac{3}{2}} d x + \int 6 x d x

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

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

\int 6 x d x = 4 x^{\frac{3}{2}}

= x^{3} - 2 x^{\frac{5}{2}} + 4 x^{\frac{3}{2}}

Add a constant to the solution

= x^{3} - 2 x^{\frac{5}{2}} + 4 x^{\frac{3}{2}} + C

(2 x - 1) d x + (3 y + 7) d y = 0

x \to 4 lim (\frac{2}{x + 5})

\frac{d}{d y} (\frac{( z x - y ) ^{2}}{x})

X \frac{9}{6}, 7

ln^{2} (x)

What is the integral of (3x^2-5x^{3/2}+6sqrt(x)) ?
The integral of (3x^2-5x^{3/2}+6sqrt(x)) is x^3-2x^{5/2}+4x^{3/2}+C