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

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

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integral of-3x^4+x^3+5-5e^x

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

- \frac{3 x ^{5}}{5} + \frac{x ^{4}}{4} + 5 x - 5 e^{x} + C

Solution steps

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

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

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

\int 5 d x = 5 x

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

= - \frac{3 x ^{5}}{5} + \frac{x ^{4}}{4} + 5 x - 5 e^{x}

Add a constant to the solution

= - \frac{3 x ^{5}}{5} + \frac{x ^{4}}{4} + 5 x - 5 e^{x} + C

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