Question and Answers Forum

IntegrationQuestion and Answers: Page 192

Question Number 85596 Answers: 1 Comments: 1

∫(((√(x+1))−1)/((√(x−1))+1)) dx

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

Question Number 85568 Answers: 4 Comments: 2

∫ _0 ^(2π) (dx/((√2)−cos x))

$$\int\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\:}}\:\frac{\mathrm{dx}}{\sqrt{\mathrm{2}}−\mathrm{cos}\:\mathrm{x}} \\ $$

Question Number 85551 Answers: 0 Comments: 1

∫ (dx/(x^2 (x^4 +1)^(3/4) ))

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

Question Number 85589 Answers: 0 Comments: 0

∫((1+4u)/(−4u^2 +2u+2))du

$$\int\frac{\mathrm{1}+\mathrm{4u}}{−\mathrm{4u}^{\mathrm{2}} +\mathrm{2u}+\mathrm{2}}\mathrm{du} \\ $$$$ \\ $$

Question Number 85488 Answers: 1 Comments: 0

∫ (dx/((x^4 +x^2 +1)^(3/4) ))

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

Question Number 85480 Answers: 1 Comments: 0

∫((csc(x))/(cos(x)+cos^3 (x)+...+cos^(2n+1) (x)))dx ∀x∈n

$$\int\frac{{csc}\left({x}\right)}{{cos}\left({x}\right)+{cos}^{\mathrm{3}} \left({x}\right)+...+{cos}^{\mathrm{2}{n}+\mathrm{1}} \left({x}\right)}{dx} \\ $$$$\forall{x}\in{n} \\ $$

Question Number 85468 Answers: 1 Comments: 0

∫ln(1−e^x ) dx

$$\int{ln}\left(\mathrm{1}−{e}^{{x}} \right)\:{dx} \\ $$

Question Number 85456 Answers: 0 Comments: 7

∫ (√(csc x )) dx?

$$\int\:\sqrt{\mathrm{csc}\:\mathrm{x}\:}\:\mathrm{dx}? \\ $$

Question Number 85441 Answers: 1 Comments: 0

∫ ((6x^4 −4)/(√(x^4 −2))) dx = ?

$$\int\:\frac{\mathrm{6x}^{\mathrm{4}} −\mathrm{4}}{\sqrt{\mathrm{x}^{\mathrm{4}} −\mathrm{2}}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 85426 Answers: 1 Comments: 4

∫ _(π/4)^0 ((sin x+cos x)/(9+16sin 2x)) dx

$$\int\:_{\frac{\pi}{\mathrm{4}}} ^{\mathrm{0}} \:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{9}+\mathrm{16sin}\:\mathrm{2}{x}}\:{dx} \\ $$

Question Number 85414 Answers: 1 Comments: 1

∫(1/(1+(√(cos(x))) )) dx

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

Question Number 85395 Answers: 1 Comments: 1

Question Number 85813 Answers: 2 Comments: 1

∫ x^2 (√(1+x^2 )) dx ?

$$\int\:\mathrm{x}^{\mathrm{2}} \:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:? \\ $$

Question Number 85391 Answers: 1 Comments: 5

Question Number 85384 Answers: 1 Comments: 1

Question Number 85383 Answers: 1 Comments: 0

∫(((sin(x))/(cos^(11) (x))))^(1/5) dx

$$\int\sqrt[{\mathrm{5}}]{\frac{{sin}\left({x}\right)}{{cos}^{\mathrm{11}} \left({x}\right)}}\:{dx} \\ $$

Question Number 85362 Answers: 1 Comments: 0

∫((−4−u)/(u^2 +5u+6))du

$$\int\frac{−\mathrm{4}−\mathrm{u}}{\mathrm{u}^{\mathrm{2}} +\mathrm{5u}+\mathrm{6}}\mathrm{du} \\ $$

Question Number 85360 Answers: 1 Comments: 0

∫(e^((1−x)×e^x ) ×e^(∫xe^x dx) )dx

$$\int\left(\mathrm{e}^{\left(\mathrm{1}−\mathrm{x}\right)×\mathrm{e}^{\mathrm{x}} } ×\mathrm{e}^{\int\mathrm{xe}^{\mathrm{x}} \mathrm{dx}} \right)\mathrm{dx} \\ $$

Question Number 85355 Answers: 1 Comments: 4

Question Number 85374 Answers: 0 Comments: 2

∫_0 ^1 ((x^7 +x^3 +1)/(x^4 +1)) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{7}} +{x}^{\mathrm{3}} +\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}\:{dx}\: \\ $$

Question Number 85323 Answers: 1 Comments: 0

∫((z−3)/(5z−10))dz

$$\int\frac{\mathrm{z}−\mathrm{3}}{\mathrm{5z}−\mathrm{10}}\mathrm{dz} \\ $$

Question Number 85321 Answers: 0 Comments: 0

Question Number 85319 Answers: 1 Comments: 0

∫((2+u)/(−u^2 −u))du

$$\int\frac{\mathrm{2}+\mathrm{u}}{−\mathrm{u}^{\mathrm{2}} −\mathrm{u}}\mathrm{du} \\ $$

Question Number 85260 Answers: 1 Comments: 1

Evaluate using cauchy′s integral ∫_c (e^(iπ) /((z^2 +4)^2 (z+1)^2 ))dz where c is a circle with ∣z−i∣=3.5 help please

$$\mathrm{Evaluate}\:\mathrm{using}\:\mathrm{cauchy}'\mathrm{s}\:\mathrm{integral}\: \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{c}} \:\frac{\mathrm{e}^{\mathrm{i}\pi} }{\left(\mathrm{z}^{\mathrm{2}} +\mathrm{4}\right)^{\mathrm{2}} \left(\mathrm{z}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dz} \\ $$$$\mathrm{where}\:\mathrm{c}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mid\mathrm{z}−\mathrm{i}\mid=\mathrm{3}.\mathrm{5} \\ $$$$ \\ $$$$\mathrm{help}\:\mathrm{please} \\ $$

Question Number 85256 Answers: 0 Comments: 3

∫ _0 ^( 1) ((sin (ln x))/(ln (x))) dx

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

Question Number 85254 Answers: 0 Comments: 0

Pg 187 Pg 188 Pg 189 Pg 190 Pg 191 Pg 192 Pg 193 Pg 194 Pg 195 Pg 196

Contact: info@tinkutara.com