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IntegrationQuestion and Answers: Page 22

Question Number 205625 Answers: 1 Comments: 0

∫_0 ^1 (√(1−x^4 ))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 205599 Answers: 1 Comments: 1

laplace transform... L { sin((√t) )} =? −−−−

$$ \\ $$$$\:{laplace}\:{transform}... \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\mathscr{L}\:\left\{\:\:{sin}\left(\sqrt{{t}}\:\right)\right\}\:=? \\ $$$$−−−− \\ $$

Question Number 205590 Answers: 0 Comments: 2

J=∫_0 ^1 (√(1−x^4 ))dx

$${J}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 205558 Answers: 1 Comments: 0

∫_0 ^(π/2) ((sin^2 4θ )/(sin^2 θ ))dθ = ?

$$\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \:\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{4}\theta\:}{\mathrm{sin}^{\mathrm{2}} \theta\:}{d}\theta\:\:=\:\:\:? \\ $$

Question Number 205506 Answers: 1 Comments: 0

∫_0 ^1 (√(1−x^4 ))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 205335 Answers: 0 Comments: 0

∫((ax+b)/((x^2 −cx+d)^n ))dx

$$\int\frac{{ax}+{b}}{\left({x}^{\mathrm{2}} −{cx}+{d}\right)^{{n}} }{dx} \\ $$

Question Number 205318 Answers: 0 Comments: 0

]^(]^ ]∡)

$$\left.\overset{\left.\overset{} {\right]}\left.\right]\measuredangle} {\right]} \\ $$

Question Number 205315 Answers: 1 Comments: 0

Question Number 205294 Answers: 1 Comments: 0

∫((3x−x^3 ))^(1/3) dx

$$\int\sqrt[{\mathrm{3}}]{\mathrm{3}{x}−{x}^{\mathrm{3}} }{dx} \\ $$

Question Number 205284 Answers: 0 Comments: 0

Question Number 205279 Answers: 1 Comments: 0

∫^(π/2) _(-π/2) ((8(√2)cosx)/((1+e^(sinx) )(1+sin^4 x)))dx=aπ+blog(3+2(√2)) then find a+b

$$\underset{-\pi/\mathrm{2}} {\int}^{\pi/\mathrm{2}} \frac{\mathrm{8}\sqrt{\mathrm{2}}{cosx}}{\left(\mathrm{1}+\overset{{sinx}} {{e}}\right)\left(\mathrm{1}+{si}\overset{\mathrm{4}} {{n}x}\right)}{dx}={a}\pi+{blog}\left(\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\right)\:{then}\:{find}\:{a}+{b} \\ $$

Question Number 205269 Answers: 2 Comments: 0

Question Number 205264 Answers: 1 Comments: 0

pls how to calculate this? ∫_(1/2) ^1 ((ln(x+1))/x)dx

$$\boldsymbol{{pls}}\:\boldsymbol{{how}}\:\boldsymbol{{to}}\:\boldsymbol{{calculate}}\:\boldsymbol{{this}}? \\ $$$$\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \frac{\boldsymbol{{ln}}\left(\boldsymbol{{x}}+\mathrm{1}\right)}{\boldsymbol{{x}}}\boldsymbol{{dx}} \\ $$

Question Number 205248 Answers: 1 Comments: 0

∫_0 ^π ((x^2 cos^2 (x)−xsin(x)−cos(x)−1)/((1+xsin(x))^2 ))dx

$$\:\:\:\int_{\mathrm{0}} ^{\pi} \:\frac{{x}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \left({x}\right)−{x}\mathrm{sin}\left({x}\right)−\mathrm{cos}\left({x}\right)−\mathrm{1}}{\left(\mathrm{1}+{x}\mathrm{sin}\left({x}\right)\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 205361 Answers: 1 Comments: 0

Question Number 205245 Answers: 1 Comments: 0

calculate ∫((3xdx)/( (√(1−x^4 )))) plsssssss

$$\boldsymbol{{calculate}} \\ $$$$\:\:\: \\ $$$$\int\frac{\mathrm{3}\boldsymbol{{xdx}}}{\:\sqrt{\mathrm{1}−\boldsymbol{{x}}^{\mathrm{4}} }} \\ $$$$\boldsymbol{{plsssssss}} \\ $$

Question Number 205216 Answers: 0 Comments: 0

∫ ((arccos^3 x)/( (√(1−x^3 )))) dx =?

$$\:\:\:\:\:\int\:\frac{\mathrm{arccos}\:^{\mathrm{3}} \mathrm{x}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{3}} }}\:\mathrm{dx}\:=? \\ $$

Question Number 205163 Answers: 1 Comments: 0

∫_0 ^1 ((sin(lnx))/(lnx))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{sin}\left({lnx}\right)}{{lnx}}{dx} \\ $$

Question Number 205151 Answers: 1 Comments: 0

find ∫_0 ^∞ ((ln^2 x)/(1+x^4 ))dx

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}^{\mathrm{2}} {x}}{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 204992 Answers: 1 Comments: 0

Is there any way to integrate: ∫ (1/( (√(ln(x))))) dx without hitting the Gauss error function or e^t^2 and e^(−t^2 ) ?

$$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{way}\:\mathrm{to}\:\mathrm{integrate}: \\ $$$$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{ln}\left({x}\right)}}\:{dx} \\ $$$$\mathrm{without}\:\mathrm{hitting}\:\mathrm{the}\:\mathrm{Gauss}\:\mathrm{error}\:\mathrm{function} \\ $$$$\mathrm{or}\:{e}^{{t}^{\mathrm{2}} } \:\mathrm{and}\:{e}^{−{t}^{\mathrm{2}} } \:? \\ $$

Question Number 204985 Answers: 1 Comments: 0

Q=∫_0 ^1 (((1−x^3 )(1−x^(33) )(1−x^(333) ))/(lnx))dx

$${Q}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(\mathrm{1}−{x}^{\mathrm{3}} \right)\left(\mathrm{1}−{x}^{\mathrm{33}} \right)\left(\mathrm{1}−{x}^{\mathrm{333}} \right)}{{lnx}}{dx} \\ $$

Question Number 204921 Answers: 1 Comments: 0

Question Number 204910 Answers: 1 Comments: 1

Question Number 204902 Answers: 2 Comments: 0

calculate ∫_0 ^1 (√(x(1−x)))dx

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

Question Number 204901 Answers: 0 Comments: 0

Question Number 204866 Answers: 1 Comments: 0

∫ ((x+3)/(x^2 (√(2x+3)))) dx=?

$$\int\:\frac{{x}+\mathrm{3}}{{x}^{\mathrm{2}} \sqrt{\mathrm{2}{x}+\mathrm{3}}}\:{dx}=? \\ $$

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