Integration of (3x(x^2+3)^4) dx

Step-by-step explanation:

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It is apparently obvious we could expand the bracket and integrate term-by-term. This method would work but is very time consuming (and you could easily make a mistake) so we use a different method: integration by substitution.

Integration by substitution involves swapping the variable for another variable which depends on x: . (We are going to choose for this question).

The very first step is to choose a suitable substitution. That is, an equation which is going to make the integration easier. There is a trick for spotting this however: if an integral contains both a term and it's derivative then use the substitution .

Your integral contains the term . The derivative is and (ignoring the constants) we see is also in the integral and so the substitution will unravel this integral!

Step 2: We must now swap the variable of integration from x to u. That means interchanging all the x's in the integrand (the term being integrated) for u's and also swapping (dx" to "du").

Then,

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The substitution has made this integral is easy to solve!

Finally we can substitute back to get the answer in terms of x:

constants mean the stopped points or the points on a graph that nothing is changing, hope this

step-by-step explanation:

the camry sales+accord sale=828,000. to make it so the two numbers are 18 thousand apart and still equal 828,000, you first need to find out what half of 828,000 is. 828,000/2=414,000. for the two numbers to equal 828,000, you have to add the same amount as you subtract from the middle. in this case, the number is 9,000 because it's half of 18,000. to equal 828,000, you have to add 9,000 to 414,000 for the camry and subtract 9,000 from 414,000 for the accord. 414,000+9,000=423,000.

414,000-9,000=405,000.

423,000+405,000=828,000.

423,000-405,000=18,

hope it