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

The integral of 4x^3+5x^4+3 is x^4+x^5+3x+C

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integral of 4x^3+5x^4+3

integral

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

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

Solution steps

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

\frac{( x + 5 )}{( - 3 x )}

sin^{3} (x) - 1

\frac{x ^{3} - x + 1}{x ^{3}}

\frac{x ^{2} ln ( x )}{e ^{x}}

8 x^{- 1}

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