document.write( "Question 819287: i'm not sure to select which topic. but what i learn is in topic integration.\r
\n" ); document.write( "\n" ); document.write( "Integrate the following functions using substitution method.
\n" ); document.write( "1.S (x+5)^7dx
\n" ); document.write( "2.S 2x(x^2+3)^5dx
\n" ); document.write( "3.S ((2t+1)e^(t^2+t) dt\r
\n" ); document.write( "\n" ); document.write( "Integrate the following functions:
\n" ); document.write( "4.S (e^x+e^2x/e^x) dx
\n" ); document.write( "5.S (3/1+2x) dx
\n" ); document.write( "

Algebra.Com's Answer #493026 by ewatrrr(24785)\"\" \"About 
You can put this solution on YOUR website!
 
\n" ); document.write( "Hi,
\n" ); document.write( "Note: \"int%28+x%5En%2Cdx%29=+x%5E%28n%2B1%29%2F%28n%2B1%29+%2B+C\"(n ≠ 1) & \"int%28+e%5Eu%2Cdu%29=+e%5Eu+%2BC\" & \"int%28+1%2Fu%2Cdu%29\"= ln|x| + C
\n" ); document.write( "Integrate the following functions using substitution method.
\n" ); document.write( "1) \"int%28+green%28%28x%2B5%29%29%5E7%2Cdx%29\" Let u = x+5, \"%28du%29%2F%28dx%29=+1\", \"%28du%29=+dx\" Then:
\n" ); document.write( "\"int%28+green%28%28x%2B5%29%29%5E7%2Cdx%29\" = \"int%28+u%5E7%2Cdu%29+=+u%5E8%2F8+%2B+C+=+highlight%28%28x%2B5%29%5E8%2F8+%2BC%29\"
\n" ); document.write( "2) \"int%28+2x%28green%28x%5E2%2B3%29%29%5E5%2Cdx%29\" Let u = x^2+3, \"%28du%29=+2x%28dx%29\"Then:
\n" ); document.write( "\"int%28+2x%28green%28x%5E2%2B3%29%29%5E5%2Cdx%29\" = \"int%28+u%5E5%2Cdu%29=+u%5E6%2F6+%2B+C+=+highlight%28+%28x%5E2%2B3%29%5E6%2F6++%2B+C%29\"
\n" ); document.write( "3) \"int%28+%282t%2B1%29e%5Egreen%28%28t%5E2%2Bt%29%29%2C+dt+%29\" Let u = t^2+t, \"%28du%29%2F%28dt%29=+2t%2B1\",\"%28du%29=+%282t%2B1%29dt\"Then:
\n" ); document.write( "\"int%28+%282t%2B1%29e%5Egreen%28%28t%5E2%2Bt%29%29%2C+dt+%29\" = \"int%28+e%5Eu%2Cdu%29=+e%5Eu+%2BC+=+highlight%28+e%5E%28t%5E2%2Bt%29%2B+C%29\"
\n" ); document.write( "4)
\n" ); document.write( "5) \"int%28+3%2F%28green%281%2B2x%29%29%2C+dx%29+\" Let u = 1 + 2x, \"%28du%29%2F%28dx%29=+2\", \"%28du%29=+2%28dx%29\" Then:
\n" ); document.write( "\"int%28+3%2F%28green%281%2B2x%29%29%2C+dx%29+\" = \"%282%2F3%29%28int%28+1%2Fu%2Cdu%29%29\"= 23 ln|u| + C = 23 ln|1+2x| + C\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );