What is the integral of 50+3x^2-3/2 sqrt(x) ?

The integral of 50+3x^2-3/2 sqrt(x) is 50x+x^3-x^{3/2}+C

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integral of 50+3x^2-3/2 sqrt(x)

\int 50 + 3 x^{2} - \frac{3}{2} x d x

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

Solution steps

\int 50 + 3 x^{2} - \frac{3}{2} 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 50 d x + \int 3 x^{2} d x - \int \frac{3}{2} x d x

\int 50 d x = 50 x

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

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

= 50 x + x^{3} - x^{\frac{3}{2}}

Add a constant to the solution

= 50 x + x^{3} - x^{\frac{3}{2}} + C

\int \frac{8 x ^{2}}{4 x ^{2} + 7} d x

\frac{d}{d x} (- \frac{4}{( 2 x + 1 ) ^{2}})

e^{s^{2}}

\int x^{3} (x^{4} + 2)^{5} d x

y = x^{5} 3^{x}

What is the integral of 50+3x^2-3/2 sqrt(x) ?
The integral of 50+3x^2-3/2 sqrt(x) is 50x+x^3-x^{3/2}+C