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IntegrationQuestion and Answers: Page 187

Question Number 87279 Answers: 3 Comments: 2

∫(x^2 /(1+x^4 ))dx

$$\int\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 87185 Answers: 3 Comments: 0

∫((2x−1)/(x(x^2 +3)))dx

$$\int\frac{\mathrm{2}{x}−\mathrm{1}}{{x}\left({x}^{\mathrm{2}} +\mathrm{3}\right)}{dx} \\ $$

Question Number 87121 Answers: 3 Comments: 0

∫_0 ^(π/2) ((1−x^4 )/(1+x^4 ))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}−{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 87103 Answers: 2 Comments: 2

∫(dx/((1+x)(√(x−x^2 ))))

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

Question Number 87086 Answers: 1 Comments: 0

Question Number 87052 Answers: 0 Comments: 4

f(x)=∫_0 ^(π/2) ((sin^2 (t))/(1+xsin^2 (t)))dt

$${f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{sin}^{\mathrm{2}} \left({t}\right)}{\mathrm{1}+{xsin}^{\mathrm{2}} \left({t}\right)}{dt} \\ $$

Question Number 87046 Answers: 1 Comments: 0

∫(dx/(sin^3 x+cos^3 x))

$$\int\frac{{dx}}{{sin}^{\mathrm{3}} {x}+{cos}^{\mathrm{3}} {x}} \\ $$

Question Number 87048 Answers: 0 Comments: 0

Express into partial fractions (x^6 /(x^(12) +1))

$${Express}\:\:{into}\:\:{partial}\:\:{fractions} \\ $$$$\:\:\:\:\:\:\:\:\frac{{x}^{\mathrm{6}} }{{x}^{\mathrm{12}} +\mathrm{1}} \\ $$

Question Number 87025 Answers: 0 Comments: 2

∫_0 ^(π/2) ((arc tan ((√2) tan x))/(tan x)) dx?

$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{arc}\:\mathrm{tan}\:\left(\sqrt{\mathrm{2}}\:\mathrm{tan}\:\mathrm{x}\right)}{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}?\: \\ $$

Question Number 87023 Answers: 0 Comments: 1

∫ (dx/(√(x^2 −8x+15))) ?

$$\int\:\:\frac{\mathrm{dx}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{8x}+\mathrm{15}}}\:?\: \\ $$

Question Number 87021 Answers: 0 Comments: 0

∫((ln(1+asin(x^2 ))/(sin(x^2 )))dx

$$\int\frac{{ln}\left(\mathrm{1}+{asin}\left({x}^{\mathrm{2}} \right)\right.}{{sin}\left({x}^{\mathrm{2}} \right)}{dx} \\ $$

Question Number 87014 Answers: 1 Comments: 1

calculate ∫_0 ^∞ (e^(−[2x]) /((x+1)^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\left[\mathrm{2}{x}\right]} }{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 87013 Answers: 0 Comments: 2

calculate ∫_0 ^∞ (e^(−[x]) /(x+1))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\left[{x}\right]} }{{x}+\mathrm{1}}{dx} \\ $$

Question Number 86998 Answers: 1 Comments: 0

∫((6e^x )/(e^(2x) −1)) dx

$$\int\frac{\mathrm{6}{e}^{{x}} }{{e}^{\mathrm{2}{x}} −\mathrm{1}}\:{dx} \\ $$

Question Number 86995 Answers: 1 Comments: 0

∫_0 ^π ((a^n sin^2 (x)+b^n cos^2 (x))/(a^(2n) sin^2 (x)+b^(2n) cos^2 (x)))dx ; a>b

$$\int_{\mathrm{0}} ^{\pi} \frac{{a}^{{n}} {sin}^{\mathrm{2}} \left({x}\right)+{b}^{{n}} {cos}^{\mathrm{2}} \left({x}\right)}{{a}^{\mathrm{2}{n}} {sin}^{\mathrm{2}} \left({x}\right)+{b}^{\mathrm{2}{n}} {cos}^{\mathrm{2}} \left({x}\right)}{dx}\:;\:{a}>{b} \\ $$

Question Number 86994 Answers: 0 Comments: 0

Question Number 86993 Answers: 1 Comments: 1

Question Number 86963 Answers: 0 Comments: 0

calculate I =∫ cos^4 x sh^2 x dx

$${calculate}\:\:{I}\:=\int\:\:{cos}^{\mathrm{4}} {x}\:{sh}^{\mathrm{2}} {x}\:{dx} \\ $$

Question Number 86957 Answers: 0 Comments: 2

find ∫ arctan(((1−u)/(1+u)))du

$${find}\:\int\:\:{arctan}\left(\frac{\mathrm{1}−{u}}{\mathrm{1}+{u}}\right){du} \\ $$

Question Number 86956 Answers: 0 Comments: 3

find ∫(1−(1/x^2 ))arctan(2x)dx

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

Question Number 86955 Answers: 2 Comments: 1

find ∫ ((arctan(x))/x)dx

$${find}\:\int\:\:\frac{{arctan}\left({x}\right)}{{x}}{dx} \\ $$

Question Number 86915 Answers: 0 Comments: 0

Question Number 86914 Answers: 0 Comments: 0

Question Number 86871 Answers: 2 Comments: 1

∫ (dx/((x^4 +1)^3 ))

$$\int\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 86853 Answers: 1 Comments: 0

∫((x^6 −x^3 +2)/(x^4 −x^2 −2))dx

$$\int\frac{{x}^{\mathrm{6}} −{x}^{\mathrm{3}} +\mathrm{2}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} −\mathrm{2}}{dx} \\ $$

Question Number 86850 Answers: 1 Comments: 1

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

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

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