Integral Problem: Help Me Integrate

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SUMMARY

The discussion centers on integrating the expression e^{x \sin x + \cos x} \left( \frac{x^4 \cos^3 x - x \sin x + \cos x}{x^2 \cos^2 x} \right) dx. Participants noted the need for clarity in the equation, specifically regarding parentheses, and suggested a substitution of u = x \sin x + \cos x to facilitate integration. The goal is to express the integral in the form e^x [f(x) + f'(x)], which indicates a focus on integration techniques involving exponential functions and derivatives.

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Homework Statement



help me integrate

Homework Equations



e^{xsinx+cosx}[x^4(cosx)^3-xsinx+cosx/x^2.(cosx)^2]dx

The Attempt at a Solution



it s to lengthy and i have still not find the form that is e^x[f(x)+f`(x)]
 
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rishiraj20006 said:

Homework Statement



help me integrate

Homework Equations



e^{xsinx+cosx}[x^4(cosx)^3-xsinx+cosx/x^2.(cosx)^2]dx

The Attempt at a Solution



it s to lengthy and i have still not find the form that is e^x[f(x)+f`(x)]

The problem you posted is not very clear to me. Are you trying to integrate:
[tex]\int e ^ {x \sin x + \cos x} \left( \frac{x ^ 4 \cos ^ 3 x - x \sin x + \cos x}{x ^ 2 \cos ^ 2 x} \right) dx[/tex]?
You seems to be missing a dew parentheses.
Is that the problem?
 
Perhaps the fact that you want it in the form of [itex]e^x [f(x)+f'(x)][/itex] hints you want to make a substitution u= x sin x + cos x?
 

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