MHT CET202210 Aug 2022Evening ShiftMathematicsIndefinite IntegrationActual
The value of 2 x¹²+5 x^9 (x^5+x^3+1 )^3 ~d x is equal to (where C is arbitrary constant.)
Options
- Ax^5 2 (x^5+x^3+1 )^2 +C
- Bx¹⁰ 2 (x^5+x^3+1 )^2 +C
- C-x^5 (x^5+x^3+1 )^2 +C
- D-x¹⁰ 2 (x^5+x^3+1 )^2 +C
Correct answer
B. x¹⁰ 2 (x^5+x^3+1 )^2 +C
Step-by-step solution
aligned & 2 x¹²+5 x^9 (x^5+x^3+1 )^3 ~d x= 2 x¹²+5 x^9 x¹⁵ (1+ 1 x^2 + 1 x^5 )^3 ~d x & = 2 x^3 + 5 x^6 (1+ 1 x^2 + 1 x^5 )^3 ~d x & = - d t t^3 = 1 2 t^2 +C [ let 1+ 1 x^2 + 1 x^5 =t ] & = 1 2 (1+ 1 x^2 + 1 x^5 )^2 +C & = x¹⁰ 2 (x^5+x^3+1 )^2 +C aligned