Is Integrating 4cos(3x) the Same as 12cos(x)?

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SUMMARY

The integral of the function 4cos(3x) is not equivalent to 12cos(x). The discussion clarifies that one cannot simply multiply through with trigonometric functions when integrating. Instead, the correct approach involves understanding the integration of cos(3x) and applying the appropriate techniques for integration, such as substitution.

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$ \displaystyle{ \int { 4 \cos(3x) } \,dx } $ .

Hi,

for this problem, is this the same as 12*cos*x?

Thanks,
 
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Hi tmt,

Nope, that's not true. You can't multiply through like that with trig functions. Start with it this way...

What is $$\int \cos(x)dx$$?

What is $$\int \cos(3x)dx$$?
 

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