Manipal MET2016MathematicsDefinite Integration
(2 x¹²+5 x^9 ) (1+x^3+x^5 )^3 d x equals
Options
- Ax¹⁰ 2 (x^5+x^3+1 )^2 +C
- Bx^2+2 x (x^5+x^3+1 ) +C
- C. (x^5+x^3+1+ (2 x¹²+5 x^9 ) +C ) ]
- DNone of the above
Correct answer
A. x¹⁰ 2 (x^5+x^3+1 )^2 +C
Step-by-step solution
Let I= 2 x¹²+5 x^9 (1+x^3+x^5 )^3 d x= 5 x⁻⁶+2 x⁻³ (1+x⁻²+x⁻⁵ )^3 d x Put 1+x⁻²+x⁻⁵=t, (-2 x⁻³-5 x⁻⁶ ) d x=d t I=- d t t^3 = 1 2 t^2 = 1 2 (1+x⁻²+x⁻⁵ )^2 = x¹⁰ 2 (x^5+x^3+1 )^2 +C