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

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

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

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

x^{4} + x^{3} + x^{2} + 5 x + C

Solution steps

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

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

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

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

\int 5 d x = 5 x

= x^{4} + x^{3} + x^{2} + 5 x

Add a constant to the solution

= x^{4} + x^{3} + x^{2} + 5 x + C

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