Use the basic integration rules to find or evaluate the integral. ∫xe5−x2dx

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Use the basic integration rules to find or evaluate the integral.  ∫xe5−x2dx

vrangett · Accepted Answer

Step 1Indefinite integral, also known as antiderivative, is a function F(x)=∫f(x)dx such that F&#039;(x)=f(x). In some cases an indefinite integral can be converted to a standard integral with appropriate substitution.For example, the integral ∫sin2xcos⁡xdx can be converted to ∫u2du with the substitution u=sin⁡x. Find an appropriate substitution for the given integral.Step 2The integral to be evaluated is ∫xe5−x2dx. Use the substitution 5−x2=u. Differentiating this gives: -2xdx=du. Apply this substitution and integrate.∫xe5−x2dx=−12∫eudu=−12eu+C=−12e5−x2+CHence, the integral is equal to −12e5−x2+C.

Cleveland Walters · Accepted Answer

∫xe5−x2dx  Substitution u=5−x2  =−12∫eudu  Now we calculate:  ∫eudu  Integral of exponential function:  ∫audu=auln⁡(a) at a=e:  =eu  We substitute the already calculated integrals:  −12∫eudu  ∫=−eu2  Reverse replacement u=5−x2  =−e5−x22  Problem solved:  ∫xe5−x2  −e5−x22+C

nick1337 · Accepted Answer

∫xe5−x2dx Transform the expression ∫−12dt Evaluate the integral −12t Substitute back −12e5−x2 Calculate −e5−x22 Add C Solution −e5−x22+C

Use the basic integration rules to find or evaluate the

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