What is the integral of 3sqrt(x)-4x ?

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

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integral of 3sqrt(x)-4x

\int 3 x - 4 x d x

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

Solution steps

\int 3 x - 4 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 d x - \int 4 x d x

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

\int 4 x d x = 2 x^{2}

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

Add a constant to the solution

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

x \to 3 - lim (\frac{2 x}{x - 3})

x \to 3 lim (lo g_{5} (x))

\frac{d}{d x} (x + y)

sin (t)

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

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