Find the indefinite integral and check the results by differentiation.

Question

Find the indefinite integral and check the results by differentiation.

∫(4x²+3)²dx

Answer 1

∫(4x²+3)²dx

⁼ ∫(16x⁴+24x² +9) dx = (16/5)x⁵ +(24/3)x³+9x+Constant

= (16/5)x⁵ +(8)x³+9x+Constant

Now take derivative of

( (16/5)x⁵ +(8)x³+9x+Constant))' = = 16x⁴ +24x²+9 which is the same as the expression under the integral.