What is the integral of (x^4-3x^{3/2}+(7/(sqrt(x)))+5) ?

The integral of (x^4-3x^{3/2}+(7/(sqrt(x)))+5) is (x^5)/5-6/5 x^{5/2}+14sqrt(x)+5x+C

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integral of (x^4-3x^{3/2}+(7/(sqrt(x)))+5)

\int (x^{4} - 3 x^{\frac{3}{2}} + (\frac{7}{x}) + 5) d x

\frac{x ^{5}}{5} - \frac{6}{5} x^{\frac{5}{2}} + 14 x + 5 x + C

Solution steps

\int x^{4} - 3 x^{\frac{3}{2}} + \frac{7}{x} + 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^{4} d x - \int 3 x^{\frac{3}{2}} d x + \int \frac{7}{x} d x + \int 5 d x

\int x^{4} d x = \frac{x ^{5}}{5}

\int 3 x^{\frac{3}{2}} d x = \frac{6}{5} x^{\frac{5}{2}}

\int \frac{7}{x} d x = 14 x

\int 5 d x = 5 x

= \frac{x ^{5}}{5} - \frac{6}{5} x^{\frac{5}{2}} + 14 x + 5 x

Add a constant to the solution

= \frac{x ^{5}}{5} - \frac{6}{5} x^{\frac{5}{2}} + 14 x + 5 x + C

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What is the integral of (x^4-3x^{3/2}+(7/(sqrt(x)))+5) ?
The integral of (x^4-3x^{3/2}+(7/(sqrt(x)))+5) is (x^5)/5-6/5 x^{5/2}+14sqrt(x)+5x+C