Question

int_{}^{}\frac{ 9 }{ 2+sinx }dx

Answer 1

\[\int\limits_{}^{}\frac{ 9 }{ 2+sinx }dx\]

Answer 2

substitute t= tan(x/2)
then sin x = 2t/(1+t^2)
dx = 1/(1+t^2)

Answer 3

reference :
http://openstudy.com/users/hartnn#/updates/50960518e4b0d0275a3ccfba

Answer 4

see first tip there....

Answer 5

can u solve that now ?

Answer 6

i'm stuck with \[9\int\limits_{}^{}\frac{ dt }{ t ^{2}+t+1 }\]

Answer 7

know the method of completing the square ?
u need to complete the square in deniminator

Answer 8

and then use 1/(x^2+a^2) formula
formula 16 from that list

Answer 9

yup it's \[(t ^{2}+\frac{ 1 }{ 2})^{2}+\frac{ 3 }{ 4 }\]
right?

Answer 10

yes :)

Answer 11

now its in the form x^2+a^2
or u can also put u=t+1/2

Answer 12

*t

Answer 13

its actually this :
\((t +\frac{ 1 }{ 2})^{2}+\frac{ 3 }{ 4 }\)

Answer 14

yes.

Answer 15

thanks got it. i'm trying the partial fractions but didn't get it, is it possible w/ partial fractions?

Answer 16

u can't factorize denominator, so no....

Answer 17

not into real factors.

Answer 18

right ?

Answer 19

ok thanks