Antiderivatives

[tuansmart]

Evaluate the indefinite integral: 8/x^4 + 4/15x
I know 8/x^4=-(8/3)x^-3
I need help on 4/15x. I know 4/15x is 4(15x^-1). If I put in zero it will be undefined. I don't know how to solve 4/15x. Can somebody help me?

 

[BigGlenntheHeavy]

$\displaystyle \int\bigg(\frac{8}{x^{4}}+\frac{4}{15x}\bigg) \ dx \ = \ 8 \int x^{-4} \ dx+\frac{4}{15} \int x^{-1} \ dx$

$\displaystyle = \ -\frac{8}{3}x^{-3}+\frac{4}{15}ln|x|+C$

$\displaystyle Note: \ 4/15x \ = \ \frac{4x}{15}; \ 4/(15x) \ = \ \frac{4}{15x}, \ I'm \ assuming \ you \ wanted \ the \ latter.$

$\displaystyle Whether \ for \ emphasis \ or \ needed, \ a \ common \ courtesy \ is \ to \ use \ grouping \ symbols \ to \ avoid \ any$

$\displaystyle \ ambiguity.$