What is the integral of (-4x^6-3x^5+5e^x) ?

The integral of (-4x^6-3x^5+5e^x) is -(4x^7)/7-(x^6)/2+5e^x+C

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integral of (-4x^6-3x^5+5e^x)

\int (- 4 x^{6} - 3 x^{5} + 5 e^{x}) d x

- \frac{4 x ^{7}}{7} - \frac{x ^{6}}{2} + 5 e^{x} + C

Solution steps

\int - 4 x^{6} - 3 x^{5} + 5 e^{x} 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^{6} d x - \int 3 x^{5} d x + \int 5 e^{x} d x

\int 4 x^{6} d x = \frac{4 x ^{7}}{7}

\int 3 x^{5} d x = \frac{x ^{6}}{2}

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

= - \frac{4 x ^{7}}{7} - \frac{x ^{6}}{2} + 5 e^{x}

Add a constant to the solution

= - \frac{4 x ^{7}}{7} - \frac{x ^{6}}{2} + 5 e^{x} + C

\frac{d}{d x} (x^{3} + 3 x^{2} - 6 x - 8)

\int \frac{( arctan ( x ) ) ^{7}}{x ^{2} + 1} d x

f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 3)

\int 4 x^{2} x + 9 d x

What is the integral of (-4x^6-3x^5+5e^x) ?
The integral of (-4x^6-3x^5+5e^x) is -(4x^7)/7-(x^6)/2+5e^x+C