IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

shinee

can u plz integrate these
1)sec⁵xtanx    ans    1/5(sec⁵x)
2)(cos2x)/(sinx +cosx)² =   ans   log lsinx+cosxl
3)(x^e-1+ e^x-1 )/(x^e+   e^x ) ans 1/e{logIx^e +e^xl}
can u also tell me how(on wat basis) we should take substitutions like t,z etc
4)(sin2x)/(sin5xsin3x) ans 1/3LogIsin3xI-1/5logIsinxI
5)(1-tanx)/(1+tanx)     ans log Icosx+sinxI
6)cot³x ans -1/2cot²x - log lsinxl
7)(sin2x)/(sin5xsin3x)   ans   1/3loglsin3xl - 1/5 loglsin5xl
8)1/(a²sin²x + b²cos²x) ans 1/ab(tan^-1(atanx/b)
9)1/(e^x + e^-x )²   ans -1/(2(1+e^2x ))
10) 1/(e^x +1)(1+e^-x )   ans -1/(1+e^x )
11)(x+2)/

(1-x² ) ans -

(1-x² ) + 2sin^-x
12)cosec⁴x ans -cotx -(cot³x)/3
13) tan³x ans -loglsecxl +(tan² x)/2

Ask & Discuss Questions with Community & Experts