# What is the anti-derivative of f(x)=2x^{8}+10x^{5}-8x^{4}-4.

## Question:

What is the anti-derivative of {eq}f(x)=2x^{8}+10x^{5}-8x^{4}-4. {/eq}

## Anti-Derivative

The indefinite integral is generally known as the anti-derivative because the value of anti-derivative is not fixed that's why we add constant C after integrating this. We will use the exponential formula to solve this question.

Given that,

$$f(x)=2x^{8}+10x^{5}-8x^{4}-4$$

Integrate both sides with respect to x

$$\int f(x)dx=2\int x^{8}dx+10\int x^{5}dx-8\int x^{4}dx-\int 4dx$$

$$F(x)=\frac{2}{9}x^{9}+\frac{10}{6}x^{6}-\frac{8}{5}x^{5}-4x+C$$

$$F(x)=\frac{2}{9}x^{9}+\frac{5}{3}x^{3}-\frac{8}{5}x^{5}-4x+C$$

Hence,

The anti-derivative of the givcen function is

$$\boxed{F(x)=\frac{2}{9}x^{9}+\frac{5}{3}x^{3}-\frac{8}{5}x^{5}-4x+C}$$