integrate the following 1) xtan-1x/(1+x2)1/2 - Maths - Integrals

Question

integrate the following
1) xtan-1x/(1+x2)1/2

Manbar Singh · Accepted Answer

Let I = ∫x tan-1x1+x2 dxTaking tan-1x as the first function and x1+x2 as the second function and using integration by parts, we getI = tan-1x × ∫x1+x2 dx - ∫ddxtan-1x∫x1+x2dx dx + CTake I1 = ∫x1+x2 dxput 1 + x2 = t⇒2x dx = dt⇒x dx = dt2 I1 = 12∫dtt = t = 1 + x2Now, I = tan-1x × 1 + x2 - ∫11+x2 × 1 + x2  dx + CI = 1+x2 tan-1x - ∫11+x2 dx + CI = 1+x2 tan-1x - log x + 1+x2 + C

integrate the following... 1) xtan-1x/(1+x2)1/2

integrate the following...

1) xtan^-1x/(1+x²)^1/2