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question 106075 again ∫((1+cosx)/((99cosx−70sinx+210)cosx−66sinx+110))dx=? using t=tan(x/2) I get −4∫(dt/(t^4 +8t^3 −22t^2 +272t−419)) can someone factorize the denominator?

$${question}\:\mathrm{106075}\:{again} \\ $$$$\int\frac{\mathrm{1}+{cosx}}{\left(\mathrm{99}{cosx}−\mathrm{70}{sinx}+\mathrm{210}\right){cosx}−\mathrm{66}{sinx}+\mathrm{110}}{dx}=? \\ $$$${using}\:{t}={tan}\left({x}/\mathrm{2}\right)\:{I}\:{get} \\ $$$$−\mathrm{4}\int\frac{{dt}}{{t}^{\mathrm{4}} +\mathrm{8}{t}^{\mathrm{3}} −\mathrm{22}{t}^{\mathrm{2}} +\mathrm{272}{t}−\mathrm{419}} \\ $$$${can}\:{someone}\:{factorize}\:{the}\:{denominator}? \\ $$

Question Number 106075 Answers: 1 Comments: 0

∫((1+cosx)/((99cosx−70sinx+210)cosx−66sinx+110))dx=?

$$\int\frac{\mathrm{1}+{cosx}}{\left(\mathrm{99}{cosx}−\mathrm{70}{sinx}+\mathrm{210}\right){cosx}−\mathrm{66}{sinx}+\mathrm{110}}{dx}=? \\ $$

Question Number 106010 Answers: 1 Comments: 0

∫ ((1+x+x^2 )/(x^2 (x+1))) dx

$$\int\:\frac{\mathrm{1}+{x}+{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)}\:{dx}\: \\ $$

Question Number 106001 Answers: 2 Comments: 0

Question Number 105983 Answers: 1 Comments: 1

∫ ((sin x dx)/(6−sin^2 x)) ?

$$\int\:\frac{\mathrm{sin}\:{x}\:{dx}}{\mathrm{6}−\mathrm{sin}\:^{\mathrm{2}} {x}}\:?\:\: \\ $$

Question Number 105969 Answers: 3 Comments: 0

∫((sinx+cosx)/(√(1+sin2x)))dx

$$\int\frac{\mathrm{sinx}+\mathrm{cosx}}{\sqrt{\mathrm{1}+\mathrm{sin2x}}}\mathrm{dx} \\ $$

Question Number 105951 Answers: 2 Comments: 0

Question Number 105940 Answers: 1 Comments: 0

∫_0 ^1 log(tanθ)dθ

$$\int_{\mathrm{0}} ^{\mathrm{1}} {log}\left({tan}\theta\right){d}\theta \\ $$

Question Number 105862 Answers: 3 Comments: 1

∫ (dx/(9+16cos^2 x)) ?

$$\int\:\frac{{dx}}{\mathrm{9}+\mathrm{16cos}\:^{\mathrm{2}} {x}}\:? \\ $$

Question Number 105815 Answers: 1 Comments: 0

Question Number 105781 Answers: 1 Comments: 1

Please, I need help. Exercise We have : J_n = ∫_0 ^( (π/4)) tan^n (x) dx 1) Establish a recurrence relation between J_(n+2) and J_n . 2) Calculate J_0 and J_1 , then deduce the expression of J_n as a function of n. The deduction of the last question, please.

$$\mathrm{Please},\:\mathrm{I}\:\mathrm{need}\:\mathrm{help}. \\ $$$$\mathrm{Exercise} \\ $$$$\mathrm{We}\:\mathrm{have}\:: \\ $$$$\mathrm{J}_{\mathrm{n}} =\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \mathrm{tan}^{\mathrm{n}} \left(\mathrm{x}\right)\:\mathrm{dx} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Establish}\:\mathrm{a}\:\mathrm{recurrence}\:\mathrm{relation} \\ $$$$\mathrm{between}\:\boldsymbol{\mathrm{J}}_{\boldsymbol{\mathrm{n}}+\mathrm{2}} \:\mathrm{and}\:\boldsymbol{\mathrm{J}}_{\boldsymbol{\mathrm{n}}} . \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Calculate}\:\boldsymbol{\mathrm{J}}_{\mathrm{0}} \:\mathrm{and}\:\boldsymbol{\mathrm{J}}_{\mathrm{1}} ,\:\mathrm{then} \\ $$$$\mathrm{deduce}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{of}\:\boldsymbol{\mathrm{J}}_{\boldsymbol{\mathrm{n}}} \:\mathrm{as}\:\mathrm{a} \\ $$$$\mathrm{function}\:\mathrm{of}\:\boldsymbol{\mathrm{n}}. \\ $$$$\mathrm{The}\:\mathrm{deduction}\:\mathrm{of}\:\mathrm{the}\:\mathrm{last} \\ $$$$\mathrm{question},\:\mathrm{please}. \\ $$

Question Number 105755 Answers: 2 Comments: 0

∫ (dx/(√(x(√x) −x^2 ))) ?

$$\int\:\frac{{dx}}{\sqrt{{x}\sqrt{{x}}\:−{x}^{\mathrm{2}} }}\:? \\ $$

Question Number 105753 Answers: 1 Comments: 1

∫ ((x^2 +sin^2 x)/(x^2 +cos^2 x)) dx

$$\int\:\frac{{x}^{\mathrm{2}} +\mathrm{sin}\:^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} +\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$

Question Number 105743 Answers: 1 Comments: 1