What is the integral of ((e^x-4x^2))/7 ?

The integral of ((e^x-4x^2))/7 is 1/7 (e^x-(4x^3)/3)+C

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integral of ((e^x-4x^2))/7

\int \frac{( e ^{x} - 4 x ^{2} )}{7} d x

\frac{1}{7} (e^{x} - \frac{4 x ^{3}}{3}) + C

Solution steps

\int \frac{e ^{x} - 4 x ^{2}}{7} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{7} \cdot \int e^{x} - 4 x^{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

= \frac{1}{7} (\int e^{x} d x - \int 4 x^{2} d x)

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

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

= \frac{1}{7} (e^{x} - \frac{4 x ^{3}}{3})

Add a constant to the solution

= \frac{1}{7} (e^{x} - \frac{4 x ^{3}}{3}) + C

What is the integral of ((e^x-4x^2))/7 ?
The integral of ((e^x-4x^2))/7 is 1/7 (e^x-(4x^3)/3)+C