What is the integral of 12x^3+1/(6sqrt(x))-3/(2x^4) ?

The integral of 12x^3+1/(6sqrt(x))-3/(2x^4) is 3x^4+1/3 sqrt(x)+1/(2x^3)+C

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integral of 12x^3+1/(6sqrt(x))-3/(2x^4)

\int 12 x^{3} + \frac{1}{6 x} - \frac{3}{2 x ^{4}} d x

3 x^{4} + \frac{1}{3} x + \frac{1}{2 x ^{3}} + C

Solution steps

\int 12 x^{3} + \frac{1}{6 x} - \frac{3}{2 x ^{4}} 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 12 x^{3} d x + \int \frac{1}{6 x} d x - \int \frac{3}{2 x ^{4}} d x

\int 12 x^{3} d x = 3 x^{4}

\int \frac{1}{6 x} d x = \frac{1}{3} x

\int \frac{3}{2 x ^{4}} d x = - \frac{1}{2 x ^{3}}

= 3 x^{4} + \frac{1}{3} x - (- \frac{1}{2 x ^{3}})

Simplify

= 3 x^{4} + \frac{1}{3} x + \frac{1}{2 x ^{3}}

Add a constant to the solution

= 3 x^{4} + \frac{1}{3} x + \frac{1}{2 x ^{3}} + C

What is the integral of 12x^3+1/(6sqrt(x))-3/(2x^4) ?
The integral of 12x^3+1/(6sqrt(x))-3/(2x^4) is 3x^4+1/3 sqrt(x)+1/(2x^3)+C