Exercise
$\int_0^1\left(4\pi x^2\sqrt{16x^2+1}\right)dx$
Step-by-step Solution
Final answer to the exercise
$12.5663706\left(1\frac{1}{64}\sqrt{\left(16\cdot 1^2+1\right)^{3}}+1\frac{3}{128}\sqrt{16\cdot 1^2+1}+\frac{3}{512}\ln\left|\sqrt{16\cdot 1^2+1}+4\cdot 1\right|+1\left(-\frac{1}{32}\right)\sqrt{16\cdot 1^2+1}-\frac{1}{128}\ln\left|\sqrt{16\cdot 1^2+1}+4\cdot 1\right|-\left(0\frac{1}{64}\sqrt{\left(16\cdot 0^2+1\right)^{3}}+0\frac{3}{128}\sqrt{16\cdot 0^2+1}+\frac{3}{512}\ln\left|\sqrt{16\cdot 0^2+1}+4\cdot 0\right|+0\left(-\frac{1}{32}\right)\sqrt{16\cdot 0^2+1}-\frac{1}{128}\ln\left|\sqrt{16\cdot 0^2+1}+4\cdot 0\right|\right)\right)$