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

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

Question

anti derivative of 
f(x)=8x^9-2x^6+12x^3

How to use formula x^(n)=(x^(n+1))/(n+1)?

.sam. · Answer

yes

.sam. · Answer

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

across · Answer

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

anonymous · Answer

$$f'\left(x\right)=a{x}^b\Rightarrow f\left(x\right)=\frac{a}{b+1}{x}^{b+1}\mid\forall\left(b\in\mathbb{R},|b|>0,b\neq-1\right)$$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 $f'\left(x\right)=5{x}^{15}$.

anonymous · Answer

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

anonymous · Answer

@Gmalavolti Yep! Good job.