AP EAMCET202017 Sep 2020Evening ShiftMathematicsIndefinite IntegrationActual
( ^3(x) ^2(x)+ (x) d x= )
Options
- A( | (x)|+ (x)+c )
- B( | (x)|+ (x)+c )
- C( | (x)|- (x)+c )
- D( | (x)|- (x)+c )
Correct answer
D. ( | (x)|- (x)+c )
Step-by-step solution
( aligned I & = ^3 x ^2 x+ x d x & = (1- ^2 x ) x ^2 x+ x d x x & =t x d x=d t I & = 1-t^2 t^2+t d t= (1-t)(1+t) t(1+t) d t & = ( 1 t -1 ) d t= t-t+C & = | x|- x+C aligned )