AP EAMCET2002MathematicsIndefinite Integration
d x 7+5 x is equal to
Options
- A1 3 ⁻¹ ( 1 3 x 2 )+c
- B1 6 ⁻¹ ( 1 6 x 2 )+c
- C1 7 ⁻¹ ( x 2 )+c
- D1 4 ⁻¹ ( x 2 )+c
Correct answer
B. 1 6 ⁻¹ ( 1 6 x 2 )+c
Step-by-step solution
Let aligned I & = d x 7+5 x & = d x 7 ( ^2 x 2 + ^2 x 2 )+5 ( ^2 x 2 - ^2 x 2 ) & = d x 12 ^2 x 2 +2 ^2 x 2 & = 1 2 ^2 x 2 6+ ^2 x 2 d x aligned Let x 2 =z aligned & 1 2 ^2 x 2 d x=d z & I= d z 6+z^2 & = 1 6 ⁻¹ z 6 +c & = 1 6 ⁻¹ ( 1 6 x 2 )+c & aligned