What is the integral of (10x^3+7/(x^2)-x) ?

The integral of (10x^3+7/(x^2)-x) is (5x^4)/2-7/x-(x^2)/2+C

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integral of (10x^3+7/(x^2)-x)

\int (10 x^{3} + \frac{7}{x ^{2}} - x) d x

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

Solution steps

\int 10 x^{3} + \frac{7}{x ^{2}} - x 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 10 x^{3} d x + \int \frac{7}{x ^{2}} d x - \int x d x

\int 10 x^{3} d x = \frac{5 x ^{4}}{2}

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

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

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

Add a constant to the solution

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

\int 2 x cos (x) - cos^{2} (x) d x

\int_{0}^{2} \frac{2}{16 - x ^{2}} d x

\int cot^{3} (4 x) d x

f (x) = \frac{4 x}{x + 2}, at x = 6

\frac{d}{d x} (3 x + 8)

What is the integral of (10x^3+7/(x^2)-x) ?
The integral of (10x^3+7/(x^2)-x) is (5x^4)/2-7/x-(x^2)/2+C