Integral Problem: Help Me Integrate

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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:
\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?
You seems to be missing a dew parentheses.
Is that the problem?
 
Perhaps the fact that you want it in the form of e^x [f(x)+f'(x)] hints you want to make a substitution u= x sin x + cos x?
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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