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

\frac{( 3 s - 4 )}{s ^{2} + 9}

\int_{0}^{9} 2 y d y

\frac{d}{d θ} (sec (θ) tan (θ))

\frac{3}{s - 9}

\frac{d}{d x} (f (x) g (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