MHT CET2012MathematicsIndefinite Integration
The value of 2 x ⁴ x+ ⁴ x d x is
Options
- A⁻¹ ( ² x )+C
- B- ⁻¹( 2 x)+C
- C⁻¹( 2 x)+C
- D⁻¹ ( ² x )+C
Correct answer
B. - ⁻¹( 2 x)+C
Step-by-step solution
Let I= 2 x ⁴ x+ ⁴ x d xI= 2 x ( ² x+ ² x )²-2 ² x ² x d xI= 2 x 1- 1 2 ( 2 x)² d x aligned =2 & 2 x 1+ (1- ² 2 x ) d x & (let t= 2 x d t=-2 2 x d x =& -d t 1+t² =&- ⁻¹ t+C =&- ⁻¹( 2 x)+C aligned