What is the antiderivative of x^2 + (5/x^5) +cos9x - e^-7x?

[sntawkin]

What is the antiderivative of x^2 + (5/x^5) +cos9x - e^-7x? I'm so lost...

and also (2x + 5sqrtx)/ x^2

 

[arildno]

An anti-derivative of a sum is a sum of anti-derivatives.

 

[colby2152]

What is the antiderivative of x^2 + (5/x^5) +cos9x - e^-7x? I'm so lost...

and also (2x + 5sqrtx)/ x^2

Well, do you know basic integration rules for powers, exponential, and trigonometric functions?

 

[HallsofIvy]

Do it one step at a time (that's what the others are saying). What is the anti-derivative of x²? What is the anti-derivative of 5x^-5? What is the anti-derivative of cos(9x)? What is the anti-derivative of e^-7x? If you don't know those, you should go back and review your basic formulas.

As for \frac{2x+ 5\sqrt{x}}{x^2}, that's really the same as
\frac{2x}{x^2}+ \frac{5x^{\frac{1}{2}}}{x^2}= 2x^{-1}+ 5x^{-\frac{3}{2}.
The anti-derivatives of those should be easy- use the first anti-derivative formula you learned!