sqrt(16+( x)^2)x dx is equal to (where C is an arbitrary constant) Option 1: 2| x + sqrt(16+( x)^2)| + xsqrt(16+( x)^2) + C Option 2: 16| x + sqrt(16+( x)^2)| + x/2sqrt(16+( x)^2) + C Option 3: 8| x + sqrt(16+( x)^2)| + x/2sqrt(16+( x)^2) + C Option 4: 4| x + sqrt(16+( x)^2)| + x/2sqrt(16+( x)^2) + C

The answer is '8| x + sqrt(16+( x)^2)| + x/2sqrt(16+( x)^2) + C'. View full solution:

sqrt(16+( x)^2)x dx is equal to (where C is an arbitrary constant)

8| x + sqrt(16+( x)^2)| + x/2sqrt(16+( x)^2) + C

2| x + sqrt(16+( x)^2)| + xsqrt(16+( x)^2) + C

16| x + sqrt(16+( x)^2)| + x/2sqrt(16+( x)^2) + C

8| x + sqrt(16+( x)^2)| + x/2sqrt(16+( x)^2) + C

4| x + sqrt(16+( x)^2)| + x/2sqrt(16+( x)^2) + C

Calculus > Integrals

Hard

core

$2\log\left|\log x + \sqrt{16+(\log x)^2}\right| + \log x\sqrt{16+(\log x)^2} + C$

$16\log\left|\log x + \sqrt{16+(\log x)^2}\right| + \frac{\log x}{2}\sqrt{16+(\log x)^2} + C$

$8\log\left|\log x + \sqrt{16+(\log x)^2}\right| + \frac{\log x}{2}\sqrt{16+(\log x)^2} + C$

$4\log\left|\log x + \sqrt{16+(\log x)^2}\right| + \frac{\log x}{2}\sqrt{16+(\log x)^2} + C$

✅ Correct Option: 3