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# Integrate $$5x^{4} + e^{-x}$$ with respect to $$x$$

### Question

Integrate $$5x^{4} + e^{-x}$$ with respect to $$x$$

### Options

A) $$-e^{-x}+x^5+k$$

B) $$e^{-x}+x^5+K$$

C) $$-e^{-x}-x^{-5}+K$$

D) $$-e^{-x}+x^4+K$$

### Explanation:

$$\int (5x^4+e^{-x})\mathit{dx}$$
$$= \frac{5x^{4+1}}{4+1}+\left(-e^{-x}\right)+c$$
$$\frac{5x^5} 5-e^{-x}+c$$
$$= x^5-e^x+c$$

## Dicussion (1)

• $$\int (5x^4+e^{-x})\mathit{dx}$$
$$= \frac{5x^{4+1}}{4+1}+\left(-e^{-x}\right)+c$$
$$\frac{5x^5} 5-e^{-x}+c$$
$$= x^5-e^x+c$$