Regroup terms.
\[6nnnfftttyy\sqrt{x}x{x}^{4}xdint\times {0}^{\imath }{e}^{-{x}^{3}}\imath \times {0}^{\imath }{e}^{-x}=\pi \times 9\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[6{n}^{1+1+1}{f}^{1+1}{t}^{1+1+1}{y}^{1+1}{x}^{\frac{1}{2}+1+4+1}dint\times {0}^{\imath }{e}^{-{x}^{3}}\imath \times {0}^{\imath }{e}^{-x}=\pi \times 9\]
Simplify \(1+1\) to \(2\).
\[6{n}^{2+1}{f}^{1+1}{t}^{2+1}{y}^{1+1}{x}^{\frac{1}{2}+1+4+1}dint\times {0}^{\imath }{e}^{-{x}^{3}}\imath \times {0}^{\imath }{e}^{-x}=\pi \times 9\]
Simplify \(2+1\) to \(3\).
\[6{n}^{3}{f}^{1+1}{t}^{3}{y}^{1+1}{x}^{\frac{1}{2}+1+4+1}dint\times {0}^{\imath }{e}^{-{x}^{3}}\imath \times {0}^{\imath }{e}^{-x}=\pi \times 9\]
Simplify \(1+1\) to \(2\).
\[6{n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{1}{2}+1+4+1}dint\times {0}^{\imath }{e}^{-{x}^{3}}\imath \times {0}^{\imath }{e}^{-x}=\pi \times 9\]
Simplify \(\frac{1}{2}+1+4+1\) to \(\frac{13}{2}\).
\[6{n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}dint\times {0}^{\imath }{e}^{-{x}^{3}}\imath \times {0}^{\imath }{e}^{-x}=\pi \times 9\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[6{n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}dint\times {0}^{\imath +\imath }{e}^{-{x}^{3}-x}\imath =\pi \times 9\]
Simplify \(\imath +\imath \) to \(2\imath \).
\[6{n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}dint\times {0}^{2\imath }{e}^{-{x}^{3}-x}\imath =\pi \times 9\]
Regroup terms.
\[6int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\pi \times 9\]
Regroup terms.
\[6int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=9\pi \]
Divide both sides by \(6\).
\[int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{9\pi }{6}\]
Simplify \(\frac{9\pi }{6}\) to \(\frac{3\pi }{2}\).
\[int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{3\pi }{2}\]
Divide both sides by \(int\).
\[{0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{\frac{3\pi }{2}}{int}\]
Simplify \(\frac{\frac{3\pi }{2}}{int}\) to \(\frac{3\pi }{2int}\).
\[{0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{3\pi }{2int}\]
Divide both sides by \({0}^{2\imath }\).
\[\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{\frac{3\pi }{2int}}{{0}^{2\imath }}\]
Simplify \(\frac{\frac{3\pi }{2int}}{{0}^{2\imath }}\) to \(\frac{3\pi }{2int\times {0}^{2\imath }}\).
\[\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{3\pi }{2int\times {0}^{2\imath }}\]
Divide both sides by \(\imath \).
\[{n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{\frac{3\pi }{2int\times {0}^{2\imath }}}{\imath }\]
Simplify \(\frac{\frac{3\pi }{2int\times {0}^{2\imath }}}{\imath }\) to \(\frac{3\pi }{2int\times {0}^{2\imath }\imath }\).
\[{n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{3\pi }{2int\times {0}^{2\imath }\imath }\]
Divide both sides by \({n}^{3}\).
\[{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{\frac{3\pi }{2int\times {0}^{2\imath }\imath }}{{n}^{3}}\]
Simplify \(\frac{\frac{3\pi }{2int\times {0}^{2\imath }\imath }}{{n}^{3}}\) to \(\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}}\).
\[{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}}\]
Divide both sides by \({f}^{2}\).
\[{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}}}{{f}^{2}}\]
Simplify \(\frac{\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}}}{{f}^{2}}\) to \(\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}}\).
\[{t}^{3}{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}}\]
Divide both sides by \({t}^{3}\).
\[{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}}}{{t}^{3}}\]
Simplify \(\frac{\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}}}{{t}^{3}}\) to \(\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}}\).
\[{y}^{2}{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}}\]
Divide both sides by \({y}^{2}\).
\[{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}}}{{y}^{2}}\]
Simplify \(\frac{\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}}}{{y}^{2}}\) to \(\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}}\).
\[{x}^{\frac{13}{2}}d{e}^{-{x}^{3}-x}=\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}}\]
Divide both sides by \({x}^{\frac{13}{2}}\).
\[d{e}^{-{x}^{3}-x}=\frac{\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}}}{{x}^{\frac{13}{2}}}\]
Simplify \(\frac{\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}}}{{x}^{\frac{13}{2}}}\) to \(\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}}\).
\[d{e}^{-{x}^{3}-x}=\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}}\]
Divide both sides by \({e}^{-{x}^{3}-x}\).
\[d=\frac{\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}}}{{e}^{-{x}^{3}-x}}\]
Simplify \(\frac{\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}}}{{e}^{-{x}^{3}-x}}\) to \(\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}{e}^{-{x}^{3}-x}}\).
\[d=\frac{3\pi }{2int\times {0}^{2\imath }\imath {n}^{3}{f}^{2}{t}^{3}{y}^{2}{x}^{\frac{13}{2}}{e}^{-{x}^{3}-x}}\]
d=(3*PI)/(2*int*0^(2*IM)*IM*n^3*f^2*t^3*y^2*x^(13/2)*e^(-x^3-x))
