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IntegrationQuestion and Answers: Page 130

Question Number 122963 Answers: 2 Comments: 0

∫_( 0) ^( 1) ((ln(1+x))/(1+x^2 ))dx

$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 123023 Answers: 1 Comments: 0

... advanced calculus... calculate::: I:=^(???) ∫_0 ^( π) (x/(1−sin(x)cos(x)))dx ................................

$$\:\:\:\:\:\:\:\:\:\:...\:{advanced}\:\:{calculus}... \\ $$$${calculate}::: \\ $$$$\:\:\:\:\:\mathrm{I}:\overset{???} {=}\:\int_{\mathrm{0}} ^{\:\pi} \frac{{x}}{\mathrm{1}−{sin}\left({x}\right){cos}\left({x}\right)}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:................................ \\ $$

Question Number 123020 Answers: 1 Comments: 0

... advanced calculus.. calculate :: ∅=∫_0 ^( π) (π/(1−sin(x)cos(x)))dx=??? ....................

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{advanced}\:\:{calculus}.. \\ $$$$ \\ $$$$\:\:\:{calculate}\:::\:\:\:\emptyset=\int_{\mathrm{0}} ^{\:\pi} \frac{\pi}{\mathrm{1}−{sin}\left({x}\right){cos}\left({x}\right)}{dx}=??? \\ $$$$\:\:\:\:\:\:\:\:.................... \\ $$

Question Number 122942 Answers: 2 Comments: 1

Question Number 122940 Answers: 1 Comments: 2

Question Number 122938 Answers: 1 Comments: 1

Question Number 122936 Answers: 1 Comments: 2

Question Number 122934 Answers: 0 Comments: 1

Question Number 122927 Answers: 1 Comments: 1

Question Number 122922 Answers: 1 Comments: 0

∫_0 ^(π/4) ((cos x+sin x)/(16sin 2x+9)) dx

$$\:\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{cos}\:{x}+\mathrm{sin}\:{x}}{\mathrm{16sin}\:\mathrm{2}{x}+\mathrm{9}}\:{dx}\: \\ $$

Question Number 122919 Answers: 2 Comments: 0

Question Number 122885 Answers: 3 Comments: 1

Question Number 122884 Answers: 1 Comments: 1

Question Number 122882 Answers: 1 Comments: 0

... nice calculus... prove that ::: Ω=∫_0 ^( 1) (((x^ϕ −1)/(ln(x))))^2 dx=(√5) ln(ϕ) .m.n.

$$\:\:\:\:\:\:\:\:\:...\:\:{nice}\:\:{calculus}... \\ $$$$\:\:\:\:{prove}\:{that}\:::: \\ $$$$\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{{x}^{\varphi} −\mathrm{1}}{{ln}\left({x}\right)}\right)^{\mathrm{2}} {dx}=\sqrt{\mathrm{5}}\:{ln}\left(\varphi\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}. \\ $$

Question Number 122877 Answers: 1 Comments: 1

∫ (sin^(−1) (x))^2 dx ?

$$\:\:\int\:\left(\mathrm{sin}^{−\mathrm{1}} \left({x}\right)\right)^{\mathrm{2}} \:{dx}\:? \\ $$

Question Number 122875 Answers: 1 Comments: 0

∫(((x^2 +1)dx)/(x^4 +x^2 +1)) = ...

$$\:\int\frac{\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}\right)\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{x}}^{\mathrm{4}} +\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}\:=\:... \\ $$$$\: \\ $$

Question Number 122867 Answers: 2 Comments: 0

Question Number 122853 Answers: 0 Comments: 2

Question Number 122838 Answers: 1 Comments: 0

∫ (dx/( (((x−1)^3 (x+2)^5 ))^(1/4) )) ?

$$\:\:\int\:\frac{{dx}}{\:\sqrt[{\mathrm{4}}]{\left({x}−\mathrm{1}\right)^{\mathrm{3}} \left({x}+\mathrm{2}\right)^{\mathrm{5}} }}\:? \\ $$

Question Number 122828 Answers: 1 Comments: 0

Question Number 122823 Answers: 1 Comments: 0

Question Number 122822 Answers: 1 Comments: 0

Question Number 122807 Answers: 1 Comments: 1

Question Number 122751 Answers: 3 Comments: 0

∫_0 ^(1/(√2)) ((x sin^(−1) (x^2 ))/( (√(1−x^4 )))) dx ?

$$\:\underset{\mathrm{0}} {\overset{\mathrm{1}/\sqrt{\mathrm{2}}} {\int}}\:\frac{{x}\:\mathrm{sin}^{−\mathrm{1}} \left({x}^{\mathrm{2}} \right)}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }}\:{dx}\:?\: \\ $$

Question Number 122748 Answers: 3 Comments: 0

∫_0 ^3 (dx/((3−x)(√(x^2 +1)))) ?

$$\:\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\frac{{dx}}{\left(\mathrm{3}−{x}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:? \\ $$

Question Number 122734 Answers: 1 Comments: 0

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