Question

Need help with intergrating these two problems
6+x^2/x dx & 2x/sq.root of x+4 dx

Answer 1

\[\int\limits_{}^{}\frac{6+x^{2}}{x}dx = \int\limits_{}^{}\frac{6}{x} + x = 6\ln x + \frac{1}{2}x^{2}+C\]

Answer 2

For 2nd one,
make the substitution
\[u = \sqrt{x+4} \rightarrow x = u^{2}-4\]
\[du = \frac{dx}{2\sqrt{x+4}}\]
\[\int\limits_{}^{}4(u^{2}-4)du = \int\limits_{}^{}4u^{2}-16 = \frac{4}{3}u^{3}-16u+C\]
substitute back in sqrt(x+4) for u

Answer 3

for the first equation yo solved how is did you get the 1/2?

Answer 4

From anti-derivative of x
\[\int\limits_{}^{}x^{n} = \frac{x^{n+1}}{n+1}\]