What is the integral of (xsqrt(x)-4x^3+5) ?

The integral of (xsqrt(x)-4x^3+5) is 2/5 x^{5/2}-x^4+5x+C

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integral of (xsqrt(x)-4x^3+5)

\int (x x - 4 x^{3} + 5) d x

\frac{2}{5} x^{\frac{5}{2}} - x^{4} + 5 x + C

Solution steps

\int x x - 4 x^{3} + 5 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 x d x - \int 4 x^{3} d x + \int 5 d x

\int x x d x = \frac{2}{5} x^{\frac{5}{2}}

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

\int 5 d x = 5 x

= \frac{2}{5} x^{\frac{5}{2}} - x^{4} + 5 x

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} - x^{4} + 5 x + C

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What is the integral of (xsqrt(x)-4x^3+5) ?
The integral of (xsqrt(x)-4x^3+5) is 2/5 x^{5/2}-x^4+5x+C