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IntegrationQuestion and Answers: Page 170

Question Number 97537 Answers: 1 Comments: 0

∫_0 ^1 ((−(√(1−x^2 )))/((yx^3 +x^2 −yx−1)))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\left({yx}^{\mathrm{3}} +{x}^{\mathrm{2}} −{yx}−\mathrm{1}\right)}{dx} \\ $$

Question Number 97531 Answers: 1 Comments: 0

5050((∫_0 ^1 (1−x^(50) )^(100) dx)/(∫_0 ^1 (1−x^(50) )^(101) dx))=

$$\mathrm{5050}\frac{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{50}} \right)^{\mathrm{100}} {dx}}{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{50}} \right)^{\mathrm{101}} {dx}}= \\ $$

Question Number 97527 Answers: 0 Comments: 0

∫((xdx)/(x!))=?

$$\int\frac{\mathrm{xdx}}{\mathrm{x}!}=? \\ $$

Question Number 97526 Answers: 1 Comments: 1

∫(dx/(1+sin x))=?

$$\int\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}=? \\ $$

Question Number 97505 Answers: 0 Comments: 0

Question Number 97439 Answers: 0 Comments: 2

∫_((√2)/2) ^1 ((x^3 /2) + (1/(6x)))(√(1+(((3x^2 )/2) −(1/(6x^2 )))^2 )) dx

$$\underset{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}} {\overset{\mathrm{1}} {\int}}\:\left(\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{6x}}\right)\sqrt{\mathrm{1}+\left(\frac{\mathrm{3x}^{\mathrm{2}} }{\mathrm{2}}\:−\frac{\mathrm{1}}{\mathrm{6x}^{\mathrm{2}} }\right)^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$

Question Number 97417 Answers: 1 Comments: 0

∫(x/(a+sin^2 x))dx=?

$$\int\frac{{x}}{{a}+\mathrm{sin}^{\mathrm{2}} \:{x}}{dx}=? \\ $$

Question Number 97400 Answers: 0 Comments: 2

∫((xdx)/(sin^2 x−3))=? help me

$$\int\frac{\mathrm{xdx}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{3}}=? \\ $$$$\:\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 97369 Answers: 1 Comments: 0

∫_0 ^1 (((ln(x))^2 )/(1+x^2 ))dx=(π^3 /(16))

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left({ln}\left({x}\right)\right)^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\frac{\pi^{\mathrm{3}} }{\mathrm{16}} \\ $$

Question Number 97361 Answers: 1 Comments: 6

∫((xdx)/(sin^2 x−3))=?

$$\int\frac{\mathrm{xdx}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{3}}=? \\ $$

Question Number 97322 Answers: 1 Comments: 0

∫sin^4 x∙cos^5 xdx=?

$$\int\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}\centerdot\mathrm{cos}\:^{\mathrm{5}} \mathrm{xdx}=? \\ $$

Question Number 97239 Answers: 0 Comments: 3

∫ ((sec^3 x dx)/(√(tan x))) ?

$$\int\:\frac{\mathrm{sec}\:^{\mathrm{3}} {x}\:{dx}}{\sqrt{\mathrm{tan}\:{x}}}\:?\: \\ $$

Question Number 97235 Answers: 1 Comments: 0

∫_0 ^1 ln(x) ln(1−x) dx ?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{ln}\left(\mathrm{x}\right)\:\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)\:\mathrm{dx}\:?\: \\ $$

Question Number 97218 Answers: 2 Comments: 0

∫_(−2) ^3 ∣x−2∣ ⌊ (x/2) ⌋ sgn (x−1) dx

$$\underset{−\mathrm{2}} {\overset{\mathrm{3}} {\int}}\:\mid{x}−\mathrm{2}\mid\:\lfloor\:\frac{{x}}{\mathrm{2}}\:\rfloor\:\mathrm{sgn}\:\left({x}−\mathrm{1}\right)\:{dx}\: \\ $$

Question Number 97153 Answers: 2 Comments: 0

Question Number 97132 Answers: 1 Comments: 1

is the formulla of sin^3 ((π/2)+x)=cos^3 x correct?

$$\mathrm{is}\:\mathrm{the}\:\mathrm{formulla}\:\mathrm{of}\:\mathrm{sin}\:^{\mathrm{3}} \left(\frac{\pi}{\mathrm{2}}+\mathrm{x}\right)=\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}\:\:\:\:\mathrm{correct}? \\ $$

Question Number 97130 Answers: 1 Comments: 0

Question Number 97109 Answers: 2 Comments: 0

∫_0 ^(π/2) ((sin^3 x)/(sin^3 x+cos^3 ×))dx=?

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

Question Number 97091 Answers: 1 Comments: 0

solve ∫x^(x+1) dx .

$${solve}\:\int{x}^{{x}+\mathrm{1}} {dx}\:. \\ $$

Question Number 97089 Answers: 1 Comments: 0

solve ∫x^x (1+ln x)dx .

$${solve}\:\:\int{x}^{{x}} \left(\mathrm{1}+\mathrm{ln}\:{x}\right){dx}\:. \\ $$

Question Number 97082 Answers: 2 Comments: 0

Question Number 97059 Answers: 0 Comments: 1

Question Number 97057 Answers: 2 Comments: 0

∫_0 ^1 (dx/(√(−ln(x)))) ? [ by Gamma function ]

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\sqrt{−\mathrm{ln}\left({x}\right)}}\:?\:\left[\:{by}\:{G}\mathrm{amma}\:\mathrm{function}\:\right] \\ $$

Question Number 97041 Answers: 2 Comments: 0

∫ sin^8 (x) cos^8 (x) dx = ?

$$\int\:\mathrm{sin}\:^{\mathrm{8}} \left({x}\right)\:\mathrm{cos}\:^{\mathrm{8}} \left({x}\right)\:{dx}\:=\:? \\ $$

Question Number 97007 Answers: 0 Comments: 16

Question Number 96990 Answers: 1 Comments: 0

∫_0 ^1 ((√x))^(√x) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\sqrt{\mathrm{x}}\right)^{\sqrt{\mathrm{x}}} \mathrm{dx} \\ $$

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