Help with integration

[SamanthaMFR]

I want to integrate this:

(Integration symbol with no limits) of (12x^5+(3/x)+(4/x^2)+4cos2x) dx

I dont have any idea of how to start, except for the first part of 12x^5 that I think it is x*(x^(6+1))/x+1

 

[HallsofIvy]

I want to integrate this:

(Integration symbol with no limits) of (12x^5+(3/x)+(4/x^2)+4cos2x) dx

I dont have any idea of how to start, except for the first part of 12x^5 that I think it is x*(x^(6+1))/x+1

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Then you really need to review! No, the integral of 12x^5 is 12(1/6)x^6+ C= 2x^6+ C. I have no idea why you think it would be what you have.

In order to integrate this you need to know that \(\displaystyle \int x^n dx= \frac{1}{n+ 1}x^{n+ 1}+ C\) for n any integer, positive or negative, except n= -1. \(\displaystyle \int \frac{1}{x} dx= \int x^{-1} dx= ln(|x|)+ C\) and \(\displaystyle \int cos(x)dx= sin(x)+ C\).

 

[Steven G]

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Then you really need to review! No, the integral of 12x^6 is 12(1/6)x^6+ C= 2x^6+ C. I have no idea why you think it would be what you have.

In order to integrate this you need to know that \(\displaystyle \int x^n dx= \frac{1}{n+ 1}x^{n+ 1}+ C\) for n any integer, positive or negative, except n= -1. \(\displaystyle \int \frac{1}{x} dx= \int x^{-1} dx= ln(|x|)+ C\) and \(\displaystyle \int cos(x)dx= sin(x)+ C\).

HallsofIvy, Be careful as int 12(x^6)dx= (12x^7)/7 +C

 

[HallsofIvy]

HallsofIvy, Be careful as int 12(x^6)dx= (12x^7)/7 +C

Actually, my error was writing x^6 for the integrand when it was x^5, but thanks for pointing that out. I have edited my response.