Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table. ∫3u2u+7du

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Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table.  ∫3u2u+7du

sonSnubsreose6v · Accepted Answer

Step 1  Given: I=∫3u2u+7du  for evaluating given integral, we simplify given expression then integrate it  so,  I=∫3u2u+7du  =32∫uduu+72  =32∫(u+72−72)du(u+72)  =32∫(1−72(u+72))du   (∵∫dxx+a=ln|x+a|+c)  =32[u−72ln|u+72|]+c  Step 2  hence, given integral is equal to 32[u−72ln|u+72|]+c.

rodclassique4r · Accepted Answer

∫3u2u+7du  Transform the expression  ∫3v−214vdv  Factor the expression  ∫3(v−7)4vdv  Use properties of integrals  34×∫v−7vdv  Separate the fraction  34×∫vv−7vdv  Divide  34×∫1−7vdv  Use properties of integrals  34×(∫1dv−∫7vdv)  Evaluate the integrals  34×(v−7ln⁡(|v|))  Substitute back  34×(2u+7−7ln⁡(|2u+7|))  Remove the parentheses  32u+214−214×ln⁡(|2u+7|)  Add c  Solution  32u+214−214×ln⁡(|2u+7|)+C

Use a table of integrals to evaluate the following indefinite

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