Evaluate the indefinite integral. ∫x6x7+2dx

Question

Evaluate the indefinite integral.  ∫x6x7+2dx

scoollato7o · Accepted Answer

Step 1  The given integral is:  ∫x6x7+2dx  Let, x7=u  Differentiate both sides of the above expression.  7x6dx=du  x6dx=du7  Substitute the above values into the given integral.  ∫x6x7+2dx=∫17(u+2)du  =17∫1u+2du  =17log|u+2|+C  Step 2  Substitute back u=x7 in the above integral.  ∫x6x7+2dx=17log|x7+2|+C  Therefore, the value of ∫x6x7+2dx is 17log|x7+2|+C

intacte87 · Accepted Answer

∫x6x7+2dx  We bring the expression 7⋅x6 under the differential sign, i.e.:  7x6dx=d(x7),t=x7  Then the original integral can be written as follows: We  ∫17(t+2)dt  ∫17x+14dx  calculate the table integral:  17∫1x+2dx=ln⁡(x+2)7  Answer:  ln⁡(x+2)7+C  or  ln⁡((x+2)17)+C  To write the final answer, it remains to substitute x7 for t.  ln⁡(x7+2)7+C

Vasquez · Accepted Answer

Given: ∫x6x7+2dx =17∫1udu ∫1udu This is the well-known tabular integral: =ln⁡(u) We substitute the already calculated integrals: 17∫1udu =ln⁡(u)7 Reverse replacement u=x7+2: =ln⁡(x7+2)7 Solution: =ln⁡(x7+2)7+C

Evaluate the indefinite integral. \int \frac{x^{6}}{x^{7}+2}dx

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