Question

anti derivative of
f(x)=8x^9-2x^6+12x^3

How to use formula x^(n)=(x^(n+1))/(n+1)?

Answer 1

yes

Answer 2

(4x^(10))/(5)-(2x^(7))/(7)+3x^(4)+C answer

Answer 3

This question is literally self explanatory. Apply that formula to each term and see what you come up with.

Answer 4

\[f'\left(x\right)=a{x}^b\Rightarrow f\left(x\right)=\frac{a}{b+1}{x}^{b+1}\mid\forall\left(b\in\mathbb{R},|b|>0,b\neq-1\right)\]You yourself have shown this identity, but it might be easier to see in LaTeX.

I won't give you any answers, but as practice, evaluate \(f\left(x\right)\) when \(f'\left(x\right)=5{x}^{15}\).

Answer 5

thank you everyone!
and @badreferences would the answer for the practice be f(x)=(5x^16)/16+C ?

Answer 6

@Gmalavolti Yep! Good job.