Question

when using the substitution u=root(1+x), an antiderivative of int(60x(root(1+x))dx) is

Answer 1

\[\int\limits_{}^{}60\sqrt{1+x}dx\]
\[u = \sqrt{1+x} \]
\[du = \frac{dx}{2\sqrt{1+x}} \rightarrow dx = 2u du\]
\[=\int\limits_{}^{}120 u^{2} du\]
\[=40u^{3} + C\]
\[=40(1+x)\sqrt{1+x} +C\]