BITSAT2014MathematicsIndefinite IntegrationActual
Evaluate: 1 1+3 ² x+8 ² x dx
Options
- A1 6 ⁻¹(2 x )+ C
- B⁻¹(2 x )+ C
- C1 6 ⁻¹ ( 2 x 3 )+ C
- DNone of these
Correct answer
C. 1 6 ⁻¹ ( 2 x 3 )+ C
Step-by-step solution
I = 1 1+3 ² x +8 ² x dx Dividing the numerator and denominator by ² x , we get I= ² x ² x+3 ² x+8 d x= ² x 4 ² x+9 d x Putting x=t ² x d x=d t, we get I = dt 4 t ²+9 = 1 4 dt t ²+(3 / 2)² = 1 4 1 3 / 2 ⁻¹ ( t 3 / 2 )+ C I = 1 6 ⁻¹ ( 2 t 3 )+ C = 1 6 ⁻¹ ( 2 x 3 )+ C