document.write( "Question 1029789: Evaluate exactly the value of the integral from negative 1 to 0 of the product of the cube of the quantity 4 times x to the 6th power plus 2 times x and 12 times x to the 5th power plus 1, dx. Your work must include the use of substitution and the antiderivative. \n" ); document.write( "

Algebra.Com's Answer #644746 by Fombitz(32388) $\"\"$ $\"About$

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$\"int%28%28%284x%5E6%2B2x%29%5E3%2812x%5E5%2B1%29%29%2Cdx%2C-1%2C0%29\"$
\n" ); document.write( "Let $\"u=4x%5E6%2B2x\"$ ,
\n" ); document.write( " $\"du=%2824x%5E5%2B2%29dx\"$
\n" ); document.write( " $\"du%2F2=%2812x%5E5%2B1%29dx\"$
\n" ); document.write( "Check the limits, when $\"x=0\"$ , $\"u=0\"$
\n" ); document.write( "When $\"x=-1\"$ , $\"u=4-2=2\"$
\n" ); document.write( "Substituting,
\n" ); document.write( "

\n" ); document.write( "

\n" ); document.write( " $\"int%28%28%284x%5E6%2B2x%29%5E3%2812x%5E5%2B1%29%29%2Cdx%2C-1%2C0%29=-u%5E4%2F8%2BC\"$
\n" ); document.write( " $\"int%28%28%284x%5E6%2B2x%29%5E3%2812x%5E5%2B1%29%29%2Cdx%2C-1%2C0%29=-2%5E4%2F8\"$
\n" ); document.write( " $\"int%28%28%284x%5E6%2B2x%29%5E3%2812x%5E5%2B1%29%29%2Cdx%2C-1%2C0%29=-16%2F8\"$
\n" ); document.write( " $\"highlight%28int%28%28%284x%5E6%2B2x%29%5E3%2812x%5E5%2B1%29%29%2Cdx%2C-1%2C0%29=-2%29\"$ \n" ); document.write( "

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