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IntegrationQuestion and Answers: Page 189

Question Number 84733 Answers: 1 Comments: 0

∫((x^4 +1)/(x^6 +1))dx

$\int \frac{x^{4} + 1}{x^{6} + 1} d x$

Question Number 84726 Answers: 0 Comments: 0

prove that ∫_0 ^1 (y^y )^((y^y )^((y^y )^.^.^. ) ) dy=(π^2 /(12))

$p r o v e t h a t$ $\int_{0}^{1} {(y^{y})}^{{(y^{y})}^{{(y^{y})}^{.^{.^{.}}}}} d y = \frac{π^{2}}{12}$

Question Number 84713 Answers: 2 Comments: 2

∫ _0 ^( 1) cos^(−1) (x^2 −x+1) dx ?

$\int {\overset{1}{}}_{0} \cos^{- 1} (x^{2} - x + 1) dx ?$

Question Number 84702 Answers: 0 Comments: 3

Question Number 84709 Answers: 1 Comments: 0

∫((tan(x)))^(1/3) dx

$\int \sqrt[3]{t a n (x)} d x$

Question Number 84708 Answers: 1 Comments: 0

Question Number 84693 Answers: 1 Comments: 1

Question Number 84685 Answers: 0 Comments: 0

∫(dx/(x(2−e^x )))

$\int \frac{d x}{x (2 - e^{x})}$

Question Number 84681 Answers: 1 Comments: 1

Question Number 84666 Answers: 1 Comments: 2

∫ x sin^(−1) (x) dx

$\int x \sin^{- 1} (x) d x$

Question Number 84580 Answers: 0 Comments: 0

find A_λ =∫ ((x+1)/(x+3))(√((λ+x)/(λ−x)))dx

$f i n d A_{λ} = \int \frac{x + 1}{x + 3} \sqrt{\frac{λ + x}{λ - x}} d x$

Question Number 84578 Answers: 0 Comments: 4

calculate ∫_0 ^(π/4) (dx/((cosx +3sinx)^2 ))

$c a l c u l a t e \int_{0}^{\frac{π}{4}} \frac{d x}{{(c o s x + 3 s i n x)}^{2}}$

Question Number 84577 Answers: 0 Comments: 2

calculate ∫ (dx/(cosx +cos(2x)+cos(3x)))

$c a l c u l a t e \int \frac{d x}{c o s x + c o s (2 x) + c o s (3 x)}$

Question Number 84574 Answers: 0 Comments: 1

calculate I_n =∫_0 ^1 sin(narcsinx)dx

$c a l c u l a t e I_{n} = \int_{0}^{1} s i n (n a r c s i n x) d x$

Question Number 84570 Answers: 1 Comments: 1

calculate ∫_1 ^(+∞) ((arctan((3/x)))/x^2 )dx

$c a l c u l a t e \int_{1}^{+ \infty} \frac{a r c t a n (\frac{3}{x})}{x^{2}} d x$

Question Number 84569 Answers: 1 Comments: 0

find ∫ (dx/(1+tan^4 x))

$f i n d \int \frac{d x}{1 + {t a n}^{4} x}$

Question Number 84566 Answers: 0 Comments: 0

Question Number 84561 Answers: 1 Comments: 0

∫_0 ^∞ ∫_0 ^∞ ((cos(x−y)−cos(x))/(xy))dx dy

$\int_{0}^{\infty} \int_{0}^{\infty} \frac{c o s (x - y) - c o s (x)}{x y} d x d y$

Question Number 84557 Answers: 0 Comments: 1

Question Number 84556 Answers: 1 Comments: 1

∫ sin^(−1) (((2x+2)/(√(4x^2 +8x+13)))) dx

$\int \sin^{- 1} (\frac{2 x + 2}{\sqrt{{4 x}^{2} + 8 x + 13}}) dx$

Question Number 84549 Answers: 1 Comments: 0

Question Number 84505 Answers: 0 Comments: 1

2)calculate I(ξ) =∫_ξ ^1 (dx/(√(1+ξx^2 −(√(1−ξx^2 ))))) 1)find lim_(ξ→0) I(ξ)

$2) c a l c u l a t e I (ξ) = \int_{ξ}^{1} \frac{d x}{\sqrt{1 + ξ x^{2} - \sqrt{1 - ξ x^{2}}}}$ $1) f i n d {l i m}_{ξ \to 0} I (ξ)$

Question Number 84498 Answers: 0 Comments: 1

∫(√x) cos(√x) dx

$\int \sqrt{x} c o s \sqrt{x} d x$

Question Number 84497 Answers: 0 Comments: 1

∫(x^2 /(1+x^5 )) dx

$\int \frac{x^{2}}{1 + x^{5}} d x$

Question Number 84467 Answers: 0 Comments: 0

∫ ln(tan^(−1) (x)) dx

$\int \ln (\tan^{- 1} (x)) dx$

Question Number 84456 Answers: 0 Comments: 1

y=ln(√((a+sin(x))/(b−sin(x)))) if ((dy/dx))^2 −tan^2 (x)=1 show that a=b

$y = l n \sqrt{\frac{a + s i n (x)}{b - s i n (x)}}$ $i f {(\frac{d y}{d x})}^{2} - {t a n}^{2} (x) = 1$ $s h o w t h a t a = b$

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