What is the integral of-3/2 x^2+3x^4-2 ?

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

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integral of-3/2 x^2+3x^4-2

\int - \frac{3}{2} x^{2} + 3 x^{4} - 2 d x

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

Solution steps

\int - \frac{3}{2} x^{2} + 3 x^{4} - 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 \frac{3}{2} x^{2} d x + \int 3 x^{4} d x - \int 2 d x

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

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

\int 2 d x = 2 x

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{1}{2} sec (x) - \frac{1}{3} csc (x))

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

\frac{d}{d x} (14 x)

t^{2} y^{^{'}} + t y = 4, y (1) = 3

x \to 3 lim (2 x^{3} - 4 x^{2} + x - 7)

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