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IntegrationQuestion and Answers: Page 23

Question Number 186198 Answers: 1 Comments: 0

∫^3 _2 ((x^2 − 1)/(1 + ^x^2 (√(2 ln(x))))) dx

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

Question Number 186196 Answers: 3 Comments: 2

∫_1 ^2 (((√(1 )) + cos (x))/( (√1) − cos (x))) dx

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

Question Number 186195 Answers: 1 Comments: 0

∫_1 ^2 ((1/2 ∙(x^2 ) )/(x (√(x^2 + 2)))) dx

$$ \\ $$$$\:\:\:\:\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\:\:\frac{\mathrm{1}/\mathrm{2}\:\centerdot\left(\boldsymbol{{x}}^{\mathrm{2}} \right)\:}{\boldsymbol{{x}}\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} \:+\:\:\mathrm{2}}}\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$

Question Number 186194 Answers: 1 Comments: 2

∫_2 ^4 ((2x^2 − 1)/(1 + (√x^2 ) − 2)) dx

$$ \\ $$$$\:\:\:\:\:\:\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\:\:\frac{\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{1}}{\mathrm{1}\:+\:\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} }\:\:−\:\:\mathrm{2}}\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$$$ \\ $$

Question Number 186193 Answers: 2 Comments: 0

∫_0 ^1 ((sin (x))/(1 + cos(x))) dx

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

Question Number 186192 Answers: 1 Comments: 0

My old problem ∫ e^(tan x) dx

$$ \\ $$$$\:\:\:\:\:\:\:\boldsymbol{{My}}\:\boldsymbol{{old}}\:\boldsymbol{{problem}} \\ $$$$\:\:\:\int\:\:\boldsymbol{{e}}^{\boldsymbol{{tan}}\:\boldsymbol{{x}}} \:\:\boldsymbol{{dx}} \\ $$

Question Number 186190 Answers: 0 Comments: 1

My old problem.. ∫_0 ^(+∞) ((tan^(−1) (1−cos(x)))/x^2 ) dx

$$ \\ $$$$\:\:\:\:\boldsymbol{{My}}\:\boldsymbol{{old}}\:\boldsymbol{{problem}}.. \\ $$$$\:\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{+\infty} {\int}}\:\:\frac{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{1}−\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\right)}{\boldsymbol{{x}}^{\mathrm{2}} }\:\:\boldsymbol{{dx}}\:\:\: \\ $$$$ \\ $$

Question Number 186181 Answers: 1 Comments: 0

∫_0 ^π (√(1+cos^2 x)) dx =?

$$\:\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\sqrt{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}\:=? \\ $$

Question Number 186171 Answers: 1 Comments: 0

[so easy] ∫ cos^2 (4x) + sin^4 (2x) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{{so}}\:\boldsymbol{{easy}}\right] \\ $$$$\:\:\:\:\:\:\:\int\:\boldsymbol{{cos}}^{\mathrm{2}} \:\left(\mathrm{4}\boldsymbol{{x}}\right)\:+\:\boldsymbol{{sin}}^{\mathrm{4}} \:\left(\mathrm{2}\boldsymbol{{x}}\right)\:\boldsymbol{{dx}}\:\:\: \\ $$$$ \\ $$

Question Number 186170 Answers: 1 Comments: 0

∫_(−2) ^2 ((tan^(−1) ( 2 − cos (x)) )/(2 + x^2 )) dx

$$ \\ $$$$\:\:\:\:\:\:\underset{−\mathrm{2}} {\overset{\mathrm{2}} {\int}}\:\:\:\:\frac{\boldsymbol{{tan}}^{−\mathrm{1}} \:\left(\:\mathrm{2}\:−\:\boldsymbol{{cos}}\:\left(\boldsymbol{{x}}\right)\right)\:\:\:\:}{\mathrm{2}\:+\:\boldsymbol{{x}}^{\mathrm{2}} }\:\:\boldsymbol{{dx}} \\ $$$$ \\ $$

Question Number 186152 Answers: 1 Comments: 0

I= ∫_2 ^𝛑 ((cos^2 (x) − 1 )/(1 + sin (x) − tan (x))) dx

$$ \\ $$$$\:\:\:\boldsymbol{{I}}=\:\:\underset{\mathrm{2}} {\overset{\boldsymbol{\pi}} {\int}}\:\:\:\frac{\boldsymbol{{cos}}^{\mathrm{2}} \:\left(\boldsymbol{{x}}\right)\:−\:\mathrm{1}\:}{\mathrm{1}\:+\:\boldsymbol{{sin}}\:\left(\boldsymbol{{x}}\right)\:−\:\boldsymbol{{tan}}\:\left(\boldsymbol{{x}}\right)}\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$$$ \\ $$

Question Number 186132 Answers: 1 Comments: 4

Question Number 186048 Answers: 0 Comments: 2

∫_a ^b (dx/( (√(b−x))+(√(x−a))))

$$\int_{{a}} ^{{b}} \frac{{dx}}{\:\sqrt{{b}−{x}}+\sqrt{{x}−{a}}} \\ $$

Question Number 185985 Answers: 2 Comments: 0

∫ (dx/( (√(sin x(1+cos x))))) =?

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

Question Number 185961 Answers: 1 Comments: 0

solve: ∫(√([x^2 −1] dx))

$${solve}: \\ $$$$\int\sqrt{\left[{x}^{\mathrm{2}} −\mathrm{1}\right]\:{dx}} \\ $$

Question Number 185959 Answers: 1 Comments: 0

solve: ∫x^(Inx) dx

$${solve}: \\ $$$$\int{x}^{{Inx}} {dx} \\ $$

Question Number 185944 Answers: 0 Comments: 2

Question Number 185935 Answers: 2 Comments: 0

∫ ((1−cos x)/((1+cos x) cos x)) dx =?

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

Question Number 185880 Answers: 2 Comments: 2

∫_0 ^(π/2) (((tan x))^(1/3) /((sin x+cos x)^2 )) dx=?

$$\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{tan}\:{x}}}{\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:{dx}=? \\ $$

Question Number 185873 Answers: 2 Comments: 0

(1) ∫πx^2 +(√((xe^π )/x^2 ))dx=? (2) ∫((ln (x)+ln (((−z)/x)))/x^z )+z^x dx=?

$$\left(\mathrm{1}\right)\:\int\pi{x}^{\mathrm{2}} +\sqrt{\frac{{xe}^{\pi} }{{x}^{\mathrm{2}} }}{dx}=? \\ $$$$\left(\mathrm{2}\right)\:\int\frac{\mathrm{ln}\:\left({x}\right)+\mathrm{ln}\:\left(\frac{−{z}}{{x}}\right)}{{x}^{{z}} }+{z}^{{x}} {dx}=? \\ $$

Question Number 185863 Answers: 1 Comments: 1

Question Number 185848 Answers: 1 Comments: 0

Question Number 185837 Answers: 0 Comments: 1

∫((cx+b^2 )/(2x))−((cx+2b^2 )/(4x))+(((cx)^2 +4b^2 )/(8x))dx=?

$$\int\frac{{cx}+{b}^{\mathrm{2}} }{\mathrm{2}{x}}−\frac{{cx}+\mathrm{2}{b}^{\mathrm{2}} }{\mathrm{4}{x}}+\frac{\left({cx}\right)^{\mathrm{2}} +\mathrm{4}{b}^{\mathrm{2}} }{\mathrm{8}{x}}{dx}=? \\ $$

Question Number 185836 Answers: 4 Comments: 0

(1) ∫_0 ^1 (dx/(2x^4 −2x^2 +1))=? (2) ∫_0 ^∞ (x^(1/4) /(1+x^2 )) dx=?

$$\:\left(\mathrm{1}\right)\:\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\mathrm{2}{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}}=? \\ $$$$\left(\mathrm{2}\right)\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{x}^{\mathrm{1}/\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}=? \\ $$

Question Number 185799 Answers: 1 Comments: 1

Question Number 185754 Answers: 0 Comments: 0

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