Question

Nl+7 dr is equal to10.(B)+x2)2 + C(C) ^x(l+x2)2 +Cx" log | X

Answer 1

Let, the given integral be f( x ).

f( x )= ∫ 1+ x 2 dx

The expression in the above integral can be written as,

f( x )= ∫ x 2 +1 dx = ∫ x 2 + ( 1 ) 2 dx

Further, simplify the function by using the formula.

∫ x 2 + a 2 dx= 1 2 x x 2 + a 2 + a 2 2 log| x+ x 2 + a 2 |+C

Integrate the function by using the above formula.

f( x )= ∫ x 2 + ( 1 ) 2 dx = x 2 x 2 + ( 1 ) 2 + ( 1 ) 2 2 log| x+ x 2 + ( 1 ) 2 |+C = x 2 1+ x 2 + 1 2 log| x+ x 2 +1 |+C

Thus, out of all the four options, option (A) is correct.