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

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

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

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

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

\int (cos (θ) - 2 sin (θ))^{2} d θ

(x - y + 2) d x - (x - y) d y = 0

x \to 0 lim ((1 + 2 x)^{\frac{5}{x}})

2 x^{3} + 2 x y + 2 y^{2} = 38, (- 1, - 4)

x \to 0 lim (\frac{sin ( x )}{x} - 1)

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