Question and Answers Forum

IntegrationQuestion and Answers: Page 204

Question Number 77751 Answers: 0 Comments: 2

calculate ∫_(−∞) ^(+∞) ((cos(e^x +e^(−x) ))/((x^2 +x+1)^2 ))dx

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

Question Number 77729 Answers: 0 Comments: 0

prove that ∫_(−π) ^π cos(2x) cos(3x) cos(4x)....cos(2005x)dx>0

$${prove}\:{that} \\ $$$$\int_{−\pi} ^{\pi} {cos}\left(\mathrm{2}{x}\right)\:{cos}\left(\mathrm{3}{x}\right)\:{cos}\left(\mathrm{4}{x}\right)....{cos}\left(\mathrm{2005}{x}\right){dx}>\mathrm{0} \\ $$

Question Number 77716 Answers: 1 Comments: 2

∫sin(x^4 ) dx

$$\int{sin}\left({x}^{\mathrm{4}} \right)\:{dx} \\ $$

Question Number 77675 Answers: 1 Comments: 0

∫_( 0) ^( ∞) 3(2x − (3/x))^2 dx

$$\int_{\:\mathrm{0}} ^{\:\:\infty} \:\mathrm{3}\left(\mathrm{2x}\:−\:\frac{\mathrm{3}}{\mathrm{x}}\right)^{\mathrm{2}} \:\mathrm{dx} \\ $$

Question Number 77608 Answers: 0 Comments: 0

∫((( ln∣tan(((nx)/2)+(π/4))∣ )^2 )/(x^2 +1)) dx ;n>0

$$\int\frac{\left(\:{ln}\mid{tan}\left(\frac{{nx}}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right)\mid\:\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}\:\:;{n}>\mathrm{0}\: \\ $$

Question Number 77603 Answers: 1 Comments: 1

∫((10x^2 −8x+1)/(x^4 −x^3 −x+1))dx

$$\int\frac{\mathrm{10}{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{1}}{{x}^{\mathrm{4}} −{x}^{\mathrm{3}} −{x}+\mathrm{1}}{dx} \\ $$$$ \\ $$

Question Number 77593 Answers: 0 Comments: 10

Question Number 77570 Answers: 1 Comments: 0

∫_( 0) ^( 1) log(((1 + x + x^2 + x^3 + x^4 )/(√(1 + (1/x) + (1/x^2 ) + (1/x^3 ) + (1/x^4 ))))) dx

$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\:\mathrm{log}\left(\frac{\mathrm{1}\:+\:\mathrm{x}\:+\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{4}} }{\sqrt{\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }}}\right)\:\mathrm{dx} \\ $$

Question Number 77552 Answers: 1 Comments: 0

∫((x−2)/(x^2 −x+1))dx = ?

$$\int\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx}\:=\:? \\ $$

Question Number 77549 Answers: 0 Comments: 2

Question Number 77536 Answers: 1 Comments: 0

find all function that satisfy ∀ p>0 ∫_0 ^∞ f(t)e^(−pt) dt= e^(−pT) with T a positive real

$$\mathrm{find}\:\mathrm{all}\:\mathrm{function}\:\mathrm{that}\:\mathrm{satisfy} \\ $$$$\:\:\forall\:\mathrm{p}>\mathrm{0}\:\:\:\int_{\mathrm{0}} ^{\infty} \mathrm{f}\left(\mathrm{t}\right)\mathrm{e}^{−\mathrm{pt}} \mathrm{dt}=\:\mathrm{e}^{−\mathrm{pT}} \:\:\:\:\:\:\mathrm{with}\:\mathrm{T}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{real} \\ $$

Question Number 77452 Answers: 0 Comments: 0

∫e^(x^3 +x^2 −1) (3x^4 +2x^2 +2x)dx

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

Question Number 77447 Answers: 1 Comments: 0

∫ tan(x) tan(2x) tan(3x) dx

$$\int\:\mathrm{tan}\left(\mathrm{x}\right)\:\mathrm{tan}\left(\mathrm{2x}\right)\:\mathrm{tan}\left(\mathrm{3x}\right)\:\mathrm{dx} \\ $$

Question Number 77424 Answers: 0 Comments: 0

∫_0 ^∞ e^((e^x −1)^t (A)) dx A and t are constant

$$\int_{\mathrm{0}} ^{\infty} {e}^{\left({e}^{{x}} −\mathrm{1}\right)^{{t}} \:\left({A}\right)} \:{dx} \\ $$$${A}\:{and}\:{t}\:{are}\:{constant} \\ $$

Question Number 77422 Answers: 1 Comments: 1

can solve ∫ (dx/(x^(17) −1)) via elementary calculus?

$$\mathrm{can}\:\mathrm{solve}\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{17}} −\mathrm{1}}\:\mathrm{via}\: \\ $$$$\mathrm{elementary}\:\mathrm{calculus}? \\ $$

Question Number 77335 Answers: 1 Comments: 4

Question Number 77323 Answers: 0 Comments: 2

Question Number 77290 Answers: 2 Comments: 3

∫ (√(x^3 + x^4 )) dx

$$\int\:\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{4}} }\:\:\mathrm{dx} \\ $$

Question Number 77269 Answers: 0 Comments: 1

what is ∫ (1/(tan^3 (x^2 −1))) dx ?

$${what}\:{is}\:\int\:\frac{\mathrm{1}}{\mathrm{tan}\:^{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{1}\right)}\:{dx}\:? \\ $$

Question Number 77242 Answers: 1 Comments: 3

prove that ∫_0 ^a (√(2+(a/x)−2(√(a/x)) ))dx=a[(1/(√2))ln((√2)+1)+1]

$${prove}\:{that} \\ $$$$\:\int_{\mathrm{0}} ^{{a}} \sqrt{\mathrm{2}+\frac{{a}}{{x}}−\mathrm{2}\sqrt{\frac{{a}}{{x}}}\:}{dx}={a}\left[\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}{ln}\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)+\mathrm{1}\right] \\ $$

Question Number 77221 Answers: 2 Comments: 0

∫ (((√(2+x)) dx)/(√x^5 )) = ?

$$\int\:\frac{\sqrt{\mathrm{2}+{x}}\:{dx}}{\sqrt{{x}^{\mathrm{5}} }}\:=\:? \\ $$

Question Number 77158 Answers: 0 Comments: 4

∫_(−2) ^( 2) (x^3 cos(x/2) + (1/2))(√(4 − x^2 )) dx

$$\int_{−\mathrm{2}} ^{\:\mathrm{2}} \:\left(\mathrm{x}^{\mathrm{3}} \:\mathrm{cos}\frac{\mathrm{x}}{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\sqrt{\mathrm{4}\:−\:\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$

Question Number 77103 Answers: 1 Comments: 1

Question Number 77089 Answers: 0 Comments: 2

Cheap ⇊ ∫(√(x/(√(x/(√(x/(...)))))))dx

$$\boldsymbol{{Cheap}}\:\downdownarrows \\ $$$$\int\sqrt{\frac{\boldsymbol{{x}}}{\sqrt{\frac{\boldsymbol{{x}}}{\sqrt{\frac{\boldsymbol{{x}}}{...}}}}}}\boldsymbol{{dx}} \\ $$$$ \\ $$$$ \\ $$

Question Number 77087 Answers: 1 Comments: 1

∫_0 ^(a/2) x^2 (a^2 −x^2 )^((−3)/2) dx Help!!!

$$\int_{\mathrm{0}} ^{\frac{\boldsymbol{{a}}}{\mathrm{2}}} \boldsymbol{{x}}^{\mathrm{2}} \left(\boldsymbol{{a}}^{\mathrm{2}} −\boldsymbol{{x}}^{\mathrm{2}} \right)^{\frac{−\mathrm{3}}{\mathrm{2}}} \boldsymbol{{dx}} \\ $$$$\boldsymbol{{Help}}!!! \\ $$$$ \\ $$

Question Number 77086 Answers: 1 Comments: 2

∫_0 ^1 xtan^(−1) xdx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {xtan}^{−\mathrm{1}} {xdx} \\ $$$$ \\ $$

Pg 199 Pg 200 Pg 201 Pg 202 Pg 203 Pg 204 Pg 205 Pg 206 Pg 207 Pg 208

Contact: info@tinkutara.com