What is the integral of x^2sqrt(x)-1 ?

The integral of x^2sqrt(x)-1 is 2/7 x^{7/2}-x+C

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integral of x^2sqrt(x)-1

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

\frac{2}{7} x^{\frac{7}{2}} - x + C

Solution steps

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

\int x^{2} x d x = \frac{2}{7} x^{\frac{7}{2}}

\int 1 d x = x

= \frac{2}{7} x^{\frac{7}{2}} - x

Add a constant to the solution

= \frac{2}{7} x^{\frac{7}{2}} - x + C

y = arcsin (\frac{3}{x ^{2}})

\frac{d}{d t} (sin^{3} (t))

\frac{d}{d x} (3 x^{2} cos (6 x))

s (t) = 4 2 t^{2} - 4 t + 7

\int (2 x - 5 x^{2}) (2 - 10 x) d x

What is the integral of x^2sqrt(x)-1 ?
The integral of x^2sqrt(x)-1 is 2/7 x^{7/2}-x+C