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

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

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

integral

5 x^{4} - 6 x^{2} + 3

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

Solution steps

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

\frac{22}{( 121 x ^{2} + 1 ) ^{2}}

\frac{2 ^{x}}{2 ^{x} ( 1 + 4 ^{x} )}

\frac{e ^{- x}}{x ^{\frac{1}{2}}}

cos^{2} (x) sin^{2} (x)

(x - 2)^{5}

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