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

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

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integral of 4x^3+3sqrt(x)+1/(x^3)

\int 4 x^{3} + 3 x + \frac{1}{x ^{3}} d x

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

Solution steps

\int 4 x^{3} + 3 x + \frac{1}{x ^{3}} 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 4 x^{3} d x + \int 3 x d x + \int \frac{1}{x ^{3}} d x

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

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

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

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

Add a constant to the solution

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

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