Question

integral help! (cal 2) posted below! thanks in advance!

Answer 1

\[\int\limits_{}^{} \frac{ 3\sec ^{2}t }{ 6+3\tan t }dt\]

Answer 2

put tan t=x
sec^2 t dt=dx

Answer 3

I think my first step should be a substitution. so im thinking the bottom somehow

Answer 4

ahh ok let me start with this

Answer 5

first take common 3 from numerator and denominator and cancel ,then substitute as above.

Answer 6

\[\int\limits_{}^{}\frac{ dx }{ 2+x }\]

Answer 7

correct now integrate.

Answer 8

i take another substitution?

Answer 9

no need when numerator is diff. of denominator
\[\int\limits \frac{ f'(x) }{ f(x) }dx=\ln \left| f(x) \right|\]

Answer 10

sorry, i am just learning this and these are some of the class examples i have written down

Answer 11

ooooh! makes sense because the derivative of lnx is 1/x