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Popular >

integral of sqrt(x)(3-5x)

Solution

\int x (3 - 5 x) d x

Solution

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

Solution steps

\int x (3 - 5 x) d x

Expand

x (3 - 5 x) : 3 x - 5 x^{\frac{3}{2}}

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

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

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

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

Add a constant to the solution

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

Popular Examples

derivative of cos^3(e^{-x})

\frac{d}{d x} (cos^{3} (e^{- x}))

integral of cos((mpix)/3)

\int cos (\frac{mπ x}{3}) d x

(\partial)/(\partial y)(2ycos(x))

\frac{\partial}{\partial y} (2 y cos (x))

y^{''}+2y^'+2y=sin(sqrt(2)x)

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (2 x)

limit as x approaches 0+of e^{-5/x}

x \to 0 + lim (e^{- \frac{5}{x}})

Frequently Asked Questions (FAQ)

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