In the given equation as follows , use a table of integrals with forms involving ln u to find the indefinite integral:- ∫(cos⁡x)esin⁡xdx

Question

In the given equation as follows , use a table of integrals with forms involving ln u to find the indefinite integral:-  ∫(cos⁡x)esin⁡xdx

turtletalk75 · Accepted Answer

Step 1  The given integral can be evaluated by the method of substitution.  We know that,  ∫exdx=ex+c  ddxsin⁡x=cos⁡x  Step 2  The given integral is,  I=∫cos⁡xesin⁡xdx.  Put,  sin⁡x=u  du=cos⁡xdx  Then,  I=∫eudu  =eu+c  =esin⁡x+c  Hence, the required expression is, esin⁡x+c.

Shawn Kim · Accepted Answer

Given:  ∫esin⁡xcos⁡(x)dx  Substitution u=sin⁡(x)⇒dudx=cos⁡(x)  =∫eudu  ∫audu=auln⁡(a) at a=e:  =eu  =esin⁡(x)  Result:  =esin⁡(x)+C

karton · Accepted Answer

∫(cos⁡(x))∗esin⁡(x)dx We put the expression cos⁡(x) under the differential sign, i.e: cos⁡(x)dx=d(sin⁡(x)),t=sin⁡(x) Then the original integral can be written as follows: ∫etdt This is a tabular integral: ∫etdt=et+C To write the final The answer is, it remains to substitute sin⁡(x) instead of t. esin⁡(x)+C

In the given equation as follows , use a table

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