What is the integral of (x^4-6x^2+5) ?

The integral of (x^4-6x^2+5) is (x^5)/5-2x^3+5x+C

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integral of (x^4-6x^2+5)

\int (x^{4} - 6 x^{2} + 5) d x

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

Solution steps

\int x^{4} - 6 x^{2} + 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 6 x^{2} d x + \int 5 d x

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

\int \frac{x + 1}{x ^{2} - 2 x + 5} d x

\int \frac{x ^{2} + 1}{( x + 1 ) ^{2} ( x - 1 ) ^{2}} d x

\int sin (\frac{nπ}{l} x) d x

\int \frac{1}{6 6 x ^{5}} d x

\int 5 x e^{3 x + 3} d x

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