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

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

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

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

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

Solution steps

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

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

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

\int C d x = C x

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

Add a constant to the solution

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

f (x) = \frac{6 x}{x ^{2} + 1}, (- 1, - 3)

\int r \cdot e^{- r^{2}} d r

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\int_{- 1}^{0} 8 \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

y^{^{'}} = - \frac{x y}{x ^{2} + y ^{2}}