What is the integral of (3/(2x^{1/2)}-2/(3x^{1/3)}) ?

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

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integral of (3/(2x^{1/2)}-2/(3x^{1/3)})

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{2}{3} x^{\frac{3}{2}} + 1)

\frac{d}{d x} (x^{3} - 3 x^{2} - 24 x + 32)

\frac{1}{0.1 s + 1}

\int (3 e^{x} + 5) d x

\frac{d}{d x} (\frac{8 x ^{6} - 125 b ^{9}}{2 x ^{2} - 5 b ^{3}})

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