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

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

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integral of x^4-6x^2-2x+4

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

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

Solution steps

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

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

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

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

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

\frac{1}{( x ^{2} - 2 x - 5 ) ^{4}}

\int_{0}^{2} \frac{1}{2} y^{2} d y

sin (\frac{t}{t + 9})

\int \frac{2 x + 1}{3 x ^{2} - 27} d x

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