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le give A_n = ∫_0 ^(π/2) ((sin((2n−1)x))/(sinx))dx and B_n =∫_0 ^(π/2) ((sin^2 (nx))/(sin^2 x))dx 1)calculate A_n 2)prove that B_(n+1) −B_n = A_(n+1) .then find B_n .

$${le}\:{give}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{sin}\left(\left(\mathrm{2}{n}−\mathrm{1}\right){x}\right)}{{sinx}}{dx}\:{and}\:{B}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{sin}^{\mathrm{2}} \left({nx}\right)}{{sin}^{\mathrm{2}} {x}}{dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{B}_{{n}+\mathrm{1}} −{B}_{{n}} =\:{A}_{{n}+\mathrm{1}} .{then}\:{find}\:{B}_{{n}} . \\ $$

Question Number 29455 Answers: 1 Comments: 1

find ∫ 3^(√(2x+1)) dx .

$${find}\:\int\:\:\mathrm{3}^{\sqrt{\mathrm{2}{x}+\mathrm{1}}} \:{dx}\:. \\ $$

Question Number 29454 Answers: 0 Comments: 1

f is a function increasing and C^1 on [a,b] prove ∫_(f(a)) ^(f(b)) f^(−1) (t)dt = ∫_a ^b x f^′ (x)dx

$${f}\:{is}\:{a}\:{function}\:{increasing}\:{and}\:{C}^{\mathrm{1}} {on}\:\left[{a},{b}\right]\:{prove} \\ $$$$\:\int_{{f}\left({a}\right)} ^{{f}\left({b}\right)} \:{f}^{−\mathrm{1}} \left({t}\right){dt}\:=\:\int_{{a}} ^{{b}} \:{x}\:{f}^{'} \left({x}\right){dx}\: \\ $$

Question Number 29451 Answers: 0 Comments: 1

find ∫_0 ^(π/4) ln(1+tanx)dx .

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{ln}\left(\mathrm{1}+{tanx}\right){dx}\:. \\ $$

Question Number 29448 Answers: 0 Comments: 0

find lim_(x→1) ∫_x ^x^2 ((cos(πt))/(ln(t)))dt .

$${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\frac{{cos}\left(\pi{t}\right)}{{ln}\left({t}\right)}{dt}\:. \\ $$

Question Number 29447 Answers: 0 Comments: 0

find A_n = ∫_0 ^∞ (dx/((1+x^2 )^n )) with n from N^★ .

$${find}\:\:\:{A}_{{n}} =\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:{with}\:{n}\:{from}\:{N}^{\bigstar} . \\ $$

Question Number 29446 Answers: 1 Comments: 1

let give a<1 find the value of f(a)= ∫_0 ^(π/2) (dx/(1−acos^2 x)).

$${let}\:{give}\:{a}<\mathrm{1}\:{find}\:{the}\:{value}\:{of} \\ $$$${f}\left({a}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{1}−{acos}^{\mathrm{2}} {x}}. \\ $$

Question Number 29445 Answers: 1 Comments: 0

find ∫ (dx/(sinx +sin(2x))) .

$${find}\:\:\:\int\:\:\:\:\:\:\:\frac{{dx}}{{sinx}\:+{sin}\left(\mathrm{2}{x}\right)}\:. \\ $$

Question Number 29444 Answers: 0 Comments: 1

find ∫_3 ^4 (dx/(x^3 −2x^2 +x−2)) .

$${find}\:\int_{\mathrm{3}} ^{\mathrm{4}} \:\:\:\:\:\:\frac{{dx}}{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +{x}−\mathrm{2}}\:. \\ $$

Question Number 29443 Answers: 1 Comments: 0

find ∫_0 ^π ((sinx)/(√(1+sin^2 x)))dx

$${find}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{sinx}}{\sqrt{\mathrm{1}+{sin}^{\mathrm{2}} {x}}}{dx} \\ $$

Question Number 29441 Answers: 0 Comments: 1

find ∫ (x^2 /((2−x^2 )(√(1−x^2 ))))dx

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

Question Number 29440 Answers: 0 Comments: 0

find ∫_0 ^π ((cosx)/((2+cosx)(3+cosx)))dx

$${find}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\:\frac{{cosx}}{\left(\mathrm{2}+{cosx}\right)\left(\mathrm{3}+{cosx}\right)}{dx} \\ $$

Question Number 29439 Answers: 1 Comments: 0

find ∫_0 ^π (dx/(2+cosx)) .

$${find}\:\int_{\mathrm{0}} ^{\pi} \:\frac{{dx}}{\mathrm{2}+{cosx}}\:. \\ $$

Question Number 29384 Answers: 0 Comments: 3

Please can it be proven by another means that ∫tan^2 xdx=tanx+x +c

$${Please}\:{can}\:{it}\:{be}\:{proven}\:{by}\:{another} \\ $$$${means}\:{that}\: \\ $$$$ \\ $$$$\:\:\:\:\:\int\mathrm{tan}\:^{\mathrm{2}} {xdx}={tanx}+{x}\:+{c} \\ $$

Question Number 29423 Answers: 0 Comments: 1

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