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

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

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integral of (5x^4-3x^2+2x+6)

\int (5 x^{4} - 3 x^{2} + 2 x + 6) d x

x^{5} - x^{3} + x^{2} + 6 x + C

Solution steps

\int 5 x^{4} - 3 x^{2} + 2 x + 6 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^{4} d x - \int 3 x^{2} d x + \int 2 x d x + \int 6 d x

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

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

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

\int 6 d x = 6 x

= x^{5} - x^{3} + x^{2} + 6 x

Add a constant to the solution

= x^{5} - x^{3} + x^{2} + 6 x + C

\int_{0}^{1} \frac{1}{v} d v

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

sec^{2} (x) - 5

n = 0 \sum \infty 0. 2^{n}

\frac{d}{d x} (- \frac{x ^{l n (x)}}{6})

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