What is the integral of 4x^3+e^x+1 ?

The integral of 4x^3+e^x+1 is x^4+e^x+x+C

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integral of 4x^3+e^x+1

\int 4 x^{3} + e^{x} + 1 d x

x^{4} + e^{x} + x + C

Solution steps

\int 4 x^{3} + e^{x} + 1 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 e^{x} d x + \int 1 d x

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

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

\int 1 d x = x

= x^{4} + e^{x} + x

Add a constant to the solution

= x^{4} + e^{x} + x + C

F (x) = 4 x^{6} (x^{4} - 6 x)

\int (5 x^{3} + 2 x^{2} - 2 x + 1) d x

\frac{x}{( 1 - x ^{2} ) ^{\frac{1}{2}}}

\frac{d}{d x} (\frac{2 π}{x})

f (x) = (3 x + 1)^{\frac{1}{2}}