What is the integral of (3x^4-5x^2+x) ?

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

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integral of (3x^4-5x^2+x)

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

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