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

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

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

\int \frac{3}{2} x - \frac{1}{x} + sin (x) - 4 x^{3} d x

x^{\frac{3}{2}} - ln ∣ x ∣ - cos (x) - x^{4} + C

Solution steps

\int \frac{3}{2} x - \frac{1}{x} + sin (x) - 4 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 \frac{3}{2} x d x - \int \frac{1}{x} d x + \int sin (x) d x - \int 4 x^{3} d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int sin (x) d x = - cos (x)

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

= x^{\frac{3}{2}} - ln ∣ x ∣ - cos (x) - x^{4}

Add a constant to the solution

= x^{\frac{3}{2}} - ln ∣ x ∣ - cos (x) - x^{4} + C

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