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IntegrationQuestion and Answers: Page 129

Question Number 123159 Answers: 3 Comments: 0

∫_( 0) ^( (π/2)) log^2 (tan(x))dx

$$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \mathrm{log}^{\mathrm{2}} \left(\mathrm{tan}\left(\mathrm{x}\right)\right)\mathrm{dx} \\ $$

Question Number 123154 Answers: 3 Comments: 0

Question Number 123060 Answers: 3 Comments: 0

.... nice calculus .... evaluate ::: Ω=^(???) ∫_(−∞) ^( ∞) (x^2 /((1+e^x )(1+e^(−x) )))dx

$$\:\:\:\:\:\:\:\:\:\:....\:\:\:{nice}\:\:{calculus}\:.... \\ $$$$\:\:\:{evaluate}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega\overset{???} {=}\int_{−\infty} ^{\:\infty} \frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}+{e}^{{x}} \right)\left(\mathrm{1}+{e}^{−{x}} \right)}{dx} \\ $$

Question Number 123037 Answers: 5 Comments: 0

∫ ((√(1−x))/(1−(√x))) dx

$$\:\:\int\:\frac{\sqrt{\mathrm{1}−{x}}}{\mathrm{1}−\sqrt{{x}}}\:{dx} \\ $$$$ \\ $$

Question Number 123034 Answers: 1 Comments: 0

Question Number 123033 Answers: 2 Comments: 1

Evaluate the integral ∫_0 ^1 ((1−x^7 ))^(1/3) − ((1−x^3 ))^(1/7) dx .

$${Evaluate}\:{the}\:{integral}\: \\ $$$$\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}^{\mathrm{7}} }\:−\:\sqrt[{\mathrm{7}}]{\mathrm{1}−{x}^{\mathrm{3}} }\:{dx}\:. \\ $$

Question Number 122980 Answers: 2 Comments: 0

∫_0 ^(ℓn 10) ((e^x (√(e^x −1)))/(e^x +8)) dx ?

$$\:\int_{\mathrm{0}} ^{\ell{n}\:\mathrm{10}} \:\frac{{e}^{{x}} \:\sqrt{{e}^{{x}} −\mathrm{1}}}{{e}^{{x}} +\mathrm{8}}\:{dx}\:? \\ $$

Question Number 122979 Answers: 1 Comments: 0

∫_0 ^π ((x sin x)/( (√(3+sin^2 x)))) dx ?

$$\:\:\int_{\mathrm{0}} ^{\pi} \frac{{x}\:\mathrm{sin}\:{x}}{\:\sqrt{\mathrm{3}+\mathrm{sin}\:^{\mathrm{2}} {x}}}\:{dx}\:? \\ $$

Question Number 122976 Answers: 4 Comments: 0

∫_1 ^( ∞) ((tan^(−1) (x))/x^2 ) dx ?

$$\:\int_{\mathrm{1}} ^{\:\infty} \:\frac{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}{{x}^{\mathrm{2}} }\:{dx}\:? \\ $$

Question Number 122967 Answers: 2 Comments: 0

∫ (x/( (√(1−x^4 )))) dx

$$\:\:\int\:\frac{{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }}\:{dx}\: \\ $$

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)) = ...

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

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