integration

∫√x+√x2+2 dx = ?

4 Answers

1
Shriya ·

the second square root is inside the first one i.e. √x^2 +2

1
gordo ·

put (x+√2+x2)1/2 = t

to get (x+√2+x2)1/2 dx= 2√(x2+2) dt

√(x2+2)=(t4+2)/2t2

so we have I= t3/3 - 2/t +c

where t=(x+√2+x2)1/2

cheers!!

1
Shriya ·

i don't know why but i am not getting √x2+2= (t4+2)/2t2

1
gordo ·

√(x+√(x2+2)) = t

(x+√(x2+2))=t2

(x2+2)=t4-2xt2+x2

x=(t4-2)/2t2

x2+2 = (t8-4t4+4+8t4)/4t4

=(t8+4t4+4)/4t4

so √(x2+2)= (t4+2)/2t2

cheers!!

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