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IntegrationQuestion and Answers: Page 55

Question Number 160597 Answers: 1 Comments: 0

∫_0 ^( (π/2)) (dx/(2−cos x)) =?

$\int_{0}^{\frac{π}{2}} \frac{dx}{2 - \cos x} = ?$

Question Number 160594 Answers: 1 Comments: 0

∫ (dx/(1−tan^2 (x))) =?

$\int \frac{dx}{1 - \tan^{2} (x)} = ?$

Question Number 160590 Answers: 0 Comments: 0

Ω:=∫_0 ^( (1/2)) (( arcsinh(x))/x) dx =^? (π^2 /(20))

$Ω := \int_{0}^{\frac{1}{2}} \frac{a r c s i n h (x)}{x} d x \overset{?}{=} \frac{π^{2}}{20}$

Question Number 160563 Answers: 1 Comments: 0

∫x{x}[x]dx=?

$\int x {x} [x] dx = ?$

Question Number 160556 Answers: 0 Comments: 0

∫_0 ^∞ ((arctg(x))/(1+x))∙(dx/( (x)^(1/4) ))=?

$\int_{0}^{\infty} \frac{arctg (x)}{1 + x} \cdot \frac{dx}{\sqrt[4]{x}} = ?$

Question Number 160551 Answers: 1 Comments: 2

∫_0 ^1 arctan x∙ln(1+x)dx=?

$\int_{0}^{1} \arctan x \cdot \ln (1 + x) dx = ?$

Question Number 160547 Answers: 1 Comments: 0

solve Ω=∫_0 ^( ∞) (( tan^( −1) ( x ))/((1+ x^( 2) )(√( x)))) dx= ? −−−−−−−−

$s o l v e$ $Ω = \int_{0}^{\infty} \frac{{t a n}^{- 1} (x)}{(1 + x^{2}) \sqrt{x}} d x = ?$ $- - - - - - - -$

Question Number 160543 Answers: 0 Comments: 0

lim_( x→ 6) (( Γ ( sin( (π/x)))−Γ ((3/x) ))/(sin( πx )))= ?

$\lim_{x \to 6} \frac{Γ (s i n (\frac{π}{x})) - Γ (\frac{3}{x})}{s i n (π x)} = ?$

Question Number 160415 Answers: 1 Comments: 0

∫_0 ^∞ (t^n /(1+t+t^2 ))dt=?

$\int_{0}^{\infty} \frac{t^{n}}{1 + t + t^{2}} dt = ?$

Question Number 160362 Answers: 0 Comments: 0

∫(x^n /( (√(x−x^2 ))))dx=?

$\int \frac{x^{n}}{\sqrt{x - x^{2}}} dx = ?$

Question Number 160358 Answers: 1 Comments: 0

∫_0 ^(π/2) ln(sinx)ln(cosx)dx

$\int_{0}^{\frac{π}{2}} \ln (\sin x) \ln (\cos x) d x$

Question Number 160349 Answers: 1 Comments: 0

find ∫(dx/(x+e^x ))=?

$f i n d \int \frac{d x}{x + e^{x}} = ?$

Question Number 160328 Answers: 0 Comments: 0

∫_1 ^( 2e) (√(((x^2 +1)/(ln x)) (√(ln x^2 )))) dx =?

$\int_{1}^{2 e} \sqrt{\frac{x^{2} + 1}{\ln x} \sqrt{\ln x^{2}}} dx = ?$

Question Number 160291 Answers: 3 Comments: 0

Ω = ∫ ((x^2 −3x+7)/((x^2 −4x+6)^2 )) dx =?

$Ω = \int \frac{x^{2} - 3 x + 7}{{(x^{2} - 4 x + 6)}^{2}} dx = ?$

Question Number 160281 Answers: 1 Comments: 0

∫_0 ^1 ((ln^2 (1−x)lnx)/x)dx=?

$\int_{0}^{1} \frac{\ln^{2} (1 - x) lnx}{x} dx = ?$

Question Number 160276 Answers: 1 Comments: 0

∫_0 ^1 ((ln(1−x)ln(x))/(1−x))dx=?

$\int_{0}^{1} \frac{\ln (1 - x) \ln (x)}{1 - x} dx = ?$

Question Number 160204 Answers: 1 Comments: 1

∫_0 ^1 (x/(1−x^3 ))=?

$\int_{0}^{1} \frac{x}{1 - x^{3}} = ?$

Question Number 160194 Answers: 1 Comments: 1

∫_0 ^1 (x/(1−x^6 ))dx=?

$\int_{0}^{1} \frac{x}{1 - x^{6}} dx = ?$

Question Number 160113 Answers: 1 Comments: 0

prove Φ:= ∫_0 ^( ∞) (( sinh(x))/(cosh^2 (x))).(1/x) dx =^(???) ((4G)/π)

$p r o v e$ $Φ := \int_{0}^{\infty} \frac{s i n h (x)}{{c o s h}^{2} (x)} . \frac{1}{x} d x \overset{? ? ?}{=} \frac{4 G}{π}$

Question Number 160013 Answers: 0 Comments: 1

∫(1/(4sin x+3cos x))dx evaluate

$\int \frac{1}{4 s i n x + 3 c o s x} d x$ $e v a l u a t e$

Question Number 159960 Answers: 1 Comments: 0

∫_0 ^( 1) ((3x^3 −x^2 +2x−4)/( (√(x^2 −3x+2)))) dx =?

$\int_{0}^{1} \frac{3 x^{3} - x^{2} + 2 x - 4}{\sqrt{x^{2} - 3 x + 2}} d x = ?$

Question Number 159931 Answers: 0 Comments: 0

Prove :: ∫_0 ^∞ ((sin^n x)/x^m )dx=(1/(Γ(m)))∫_0 ^∞ ((D^(m−1) sin^n x)/x)dx n+m∈Odd Number.

$Prove :: \int_{0}^{\infty} \frac{\sin^{n} x}{x^{m}} dx = \frac{1}{Γ (m)} \int_{0}^{\infty} \frac{D^{m - 1} \sin^{n} x}{x} dx$ $n + m \in Odd Number .$

Question Number 159917 Answers: 0 Comments: 1

Question Number 159915 Answers: 0 Comments: 1

∫_1 ^(16) ((√x)/(1+(x^3 )^(1/4) )) dx =?

$\int_{1}^{16} \frac{\sqrt{x}}{1 + \sqrt[4]{x^{3}}} d x = ?$

Question Number 159870 Answers: 1 Comments: 0

∫ ((1−cot^2 x)/(1+sin x)) dx =?

$\int \frac{1 - \cot^{2} x}{1 + \sin x} d x = ?$

Question Number 159823 Answers: 2 Comments: 0

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