Thread: Hard Integrals
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Old January 3rd, 2009, 09:59 AM
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Quote:
Originally Posted by Ment View Post
Please, help me solution these integrals:

1.{\text{ }}\int {\frac{{\sin x\cos x}}{{\sin ^4 x + \cos ^4 x}}dx} .

2.{\text{ }}\int {\frac{{\arctan e^x }}{{\cosh x}}} dx.

3.{\text{ }}\int {\frac{{\cos x}}{{\sqrt {1 + \sin x + \cos ^2 x} }}dx} .

4.{\text{ }}\int {\frac{{dx}}{{a + b\cos x}}} {\text{ if }}1){\text{ }}a > 0{\text{ }} \wedge {\text{ }}b > 0;{\text{ }}2){\text{ }}a > 0{\text{ }} \wedge {\text{ }}b < 0.
Some hints:
(1) try using \sin^2x + \cos^2 x = 1

(2) try using u = e^x

(1) try using u = \sin x and use a trig identity

(1) try using x = 2 \tan^{-1} u
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