AP EAMCET202420 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
3 x^9+7 x^8 (x^2+2 x+5 x^8 )^2 d x=
Options
- Ax^7 5 x^7+x+2 +c
- Bx^7 2 (5 x^7+x+2 ) +c
- C1 2 (5 x^7+x+2 ) +c
- D-x^7 2 (5 x^7+x+2 ) +c
Correct answer
B. x^7 2 (5 x^7+x+2 ) +c
Step-by-step solution
I= 3 x^9+7 x^8 (x^2+2 x+5 x^8 )^2 d xI= 3 x^9+7 x^8 x¹⁶ ( 1 x^6 + 2 x^7 +5 )^2 d x I= 3 x⁻⁷+7 x⁻⁸ ( 1 x^6 + 2 x^7 +5 )^2 d x Let 1 x^6 + 2 x^7 +5=t (-6 x⁻⁷-14 x⁻⁸ ) d x=d t I= -1 2 1 t^2 d t I= 1 2 t +C I= 1 2 ( 1 x^6 + 2 x^7 +5 ) +C I= x^7 2 (x+2+5 x^7 ) +C