Manipal MET2011MathematicsIndefinite Integration
x^2 (x^2+2 ) (x^2+3 ) d x is equal to
Options
- A- 2 ⁻¹ ( x 2 )+ 3 ⁻¹ ( x 3 )+C
- B2 ⁻¹ ( x 2 )+ 3 ⁻¹ ( x 3 )+C
- C- 2 ⁻¹ x+ 3 ⁻¹ x+C
- DNone of the above
Correct answer
A. - 2 ⁻¹ ( x 2 )+ 3 ⁻¹ ( x 3 )+C
Step-by-step solution
x^2 (x^2+2 ) (x^2+3 ) d x= ( 3 x^2+3 - 2 x^2+2 ) d x= 3 3 ⁻¹ ( x 3 )- 2 2 ⁻¹ ( x 2 )+C= 3 ⁻¹ ( x 3 )- 2 ⁻¹ ( x 2 )+C