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

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

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integral of 3*sqrt(x)-4x

\int 3 \cdot 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

\frac{d ^{2}}{d x ^{2}} (- t^{3} + 15 t^{2} + 21 t)

\int \frac{( 7 sin ^{3} ( x ) )}{cos ( x )} d x

n = 0 \sum \infty n (sin (\frac{1}{n}))

f (x) = cot^{3} (4 x)

(\frac{( x + 2 )}{x - 2})^{2}

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