What is the integral of 8x^3+1/(2x^2) ?

The integral of 8x^3+1/(2x^2) is 2x^4-1/(2x)+C

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integral of 8x^3+1/(2x^2)

\int 8 x^{3} + \frac{1}{2 x ^{2}} d x

2 x^{4} - \frac{1}{2 x} + C

Solution steps

\int 8 x^{3} + \frac{1}{2 x ^{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 8 x^{3} d x + \int \frac{1}{2 x ^{2}} d x

\int 8 x^{3} d x = 2 x^{4}

\int \frac{1}{2 x ^{2}} d x = - \frac{1}{2 x}

= 2 x^{4} - \frac{1}{2 x}

Add a constant to the solution

= 2 x^{4} - \frac{1}{2 x} + C

\int e^{- c o s (x)} sin^{3} (x) d x

x \to 0 lim (cot (x))

\frac{d}{d y} (2 y - 1)

y^{^{''}} - 2 y^{^{'}} + 1 y = 0, y (0) = - 1, y^{^{'}} (0) = 2

\int \frac{1}{cos ^{2} ( x )} d x

What is the integral of 8x^3+1/(2x^2) ?
The integral of 8x^3+1/(2x^2) is 2x^4-1/(2x)+C