What is the integral of (5xsqrt(x)-1/(x^3)+3) ?

The integral of (5xsqrt(x)-1/(x^3)+3) is 2x^{5/2}+1/(2x^2)+3x+C

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integral of (5xsqrt(x)-1/(x^3)+3)

\int (5 x x - \frac{1}{x ^{3}} + 3) d x

2 x^{\frac{5}{2}} + \frac{1}{2 x ^{2}} + 3 x + C

Solution steps

\int 5 x x - \frac{1}{x ^{3}} + 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 x d x - \int \frac{1}{x ^{3}} d x + \int 3 d x

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

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

\int 3 d x = 3 x

= 2 x^{\frac{5}{2}} - (- \frac{1}{2 x ^{2}}) + 3 x

Simplify

= 2 x^{\frac{5}{2}} + \frac{1}{2 x ^{2}} + 3 x

Add a constant to the solution

= 2 x^{\frac{5}{2}} + \frac{1}{2 x ^{2}} + 3 x + C

\int (\frac{x ^{2} + 2}{2 x}) d x

\int \frac{4}{( x - 8 ) ( x - 4 )} d x

\int \frac{5}{6 - 4 x} d x

What is the integral of (5xsqrt(x)-1/(x^3)+3) ?
The integral of (5xsqrt(x)-1/(x^3)+3) is 2x^{5/2}+1/(2x^2)+3x+C