- #1

iamsmooth

- 103

- 0

So I have an integral say:

[tex]

\int \! \cos 3x dx[/tex]

The antiderivative is

[tex]\frac{1}{3}\sin (3x) + K[/tex]

But it's not obvious to me how to eye it. What I normally do is try to look for a derivative of something within the integral, so I'd know it's a result of a chain rule, but this function doesn't have it. Then I try integration by parts and it just becomes a whole big mess. I also tried the opposite rule of differentiation where you just raise the exponent by 1, then divide by the exponent, which doen't work in this case since it's not an easy polynomial.

Finally, I'm out of options and I do guessing and checking by doing semi random functions and differentiating them to see if I get the integral, and if I do, I've found the antiderivative.

There's got to be a better way to interpret this problem. I think I'm just not thinking of it correctly. Can anyone give me some pointers?

[tex]

\int \! \cos 3x dx[/tex]

The antiderivative is

[tex]\frac{1}{3}\sin (3x) + K[/tex]

But it's not obvious to me how to eye it. What I normally do is try to look for a derivative of something within the integral, so I'd know it's a result of a chain rule, but this function doesn't have it. Then I try integration by parts and it just becomes a whole big mess. I also tried the opposite rule of differentiation where you just raise the exponent by 1, then divide by the exponent, which doen't work in this case since it's not an easy polynomial.

Finally, I'm out of options and I do guessing and checking by doing semi random functions and differentiating them to see if I get the integral, and if I do, I've found the antiderivative.

There's got to be a better way to interpret this problem. I think I'm just not thinking of it correctly. Can anyone give me some pointers?

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