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

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