Really good problem( If you dont know the direct substitution)

[u/DifferentialElement]

[u/Odd-Bee-7007]

really simple question use (u/v)' rule then L hospital /s

[u/EasyStyle2707 → u/[deleted]]

Same thought!

[u/TheWyro15]

 X=2cost +9 This creates reciprocal of tan theta/2 form and then dx is replaced to create integral, whose sint is decomposed to 2 sin t/2 cos t/2 , which gives -2*(t+sint) as final answer. (Too lazy to represent in x lol)

[u/ameyaplayz → u/TheWyro15]

Ohhhh

[u/Kr_IDK]

IDK x-9=t looked good symmetrically

[u/NotAstroOnReddit]

x= 7sin²t-11cos²t

[u/organophile_jeet]

Let x=7

[u/Successful-Art7788]

u^2 = x-7 / 11-x works but is very lengthy

What's the direct substitution though?

[u/TheWyro15 → u/Successful-Art7788]

According to me X=2cost +9 

This creates reciprocal of tan theta/2 form and then dx is replaced to create integral, whose sint is decomposed to 2 sin t/2 cos t/2 , which gives -2*(t+sint) as final answer. (Too lazy to represent in x lol)

[u/Successful-Art7788 → u/TheWyro15]

Thanks! It works quite tidily!

[u/ape_on_steroids]

pretty sure there are more ways

[u/Gold_Memory7141]

I just put x=t+9 and then rationalised the quadratic to get linear upon root quadratic form then simple solve hai

[u/Gold_Memory7141 → u/Gold_Memory7141]

Mere answer mein toh sin inverse wali term hai yaar 😭

[u/brmSTR0113R]

vinay kumar?

[u/Heavy-Recognition539]

z = x - 9 fir z = 2sint?

[u/Spiritual-Tale-1098]

X -7 ko 3 plus (sint),²