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

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

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

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

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

Solution steps

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

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

\int 2 x d x = \frac{4}{3} x^{\frac{3}{2}}

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

\int 3 d x = 3 x

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

Add a constant to the solution

= 2 x^{\frac{5}{2}} + \frac{4}{3} x^{\frac{3}{2}} - \frac{7 x ^{2}}{2} + 3 x + C

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