Question

I have a question about this integral.

Answer 1

\[\int\limits \frac{ 1 }{ 1+9x ^{2} } = \frac{ \tan^{-1}(9X) }{ 9 }\]

Answer 2

Write out the integral as: \(\large \int \frac{1}{1+9x^2}dx=\int \frac{1}{1+(3x)^2}dx \)

Answer 3

\[\tan^{-1} (3x) + C\]

Answer 4

looks good. ^^

Answer 5

I have another question when i have to solve an integral with by parts i always have trouble in deciding what U should be.

Answer 6

For example: \[\int\limits (x ^{2}+1)\cos(x ^{3}+3x) \]