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IntegrationQuestion and Answers: Page 150

Question Number 103974 Answers: 2 Comments: 0

calculate ∫_(−∞) ^(+∞) (dx/((x^2 −x+1)(x^2 +3)^2 ))

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

Question Number 103871 Answers: 1 Comments: 2

∫_0 ^1 ((x^(98) −99x+98)/(logx))dx

$\int_{0}^{1} \frac{x^{98} - 99 x + 98}{l o g x} d x$

Question Number 103863 Answers: 8 Comments: 0

Question Number 103860 Answers: 2 Comments: 0

find ∫ (dx/(cos^4 x))

$find \int \frac{dx}{\cos^{4} x}$

Question Number 103846 Answers: 0 Comments: 2

∫(dx/(x^(1/3) +2))

$\int \frac{d x}{x^{\frac{1}{3}} + 2}$

Question Number 103825 Answers: 7 Comments: 0

∫ (dx/((1−sinx)^2 )) ?

$\int \frac{d x}{{(1 - s i n x)}^{2}} ?$

Question Number 103773 Answers: 1 Comments: 0

∫_c ((x^2 +2xy^2 )dx+(x^2 y^2 −1)dy) where C is the boundary of region define by y^2 = 4x and y =1 ?

$\int_{c} ((x^{2} + 2 {x y}^{2}) d x + (x^{2} y^{2} - 1) d y)$ $w h e r e C i s t h e b o u n d a r y o f$ $r e g i o n d e f i n e b y y^{2} = 4 x a n d y$ $= 1 ?$

Question Number 103742 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/((2x+1)^4 (x+3)^5 ))

$calculate \int_{0}^{\infty} \frac{dx}{{(2 x + 1)}^{4} {(x + 3)}^{5}}$

Question Number 103741 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((arctan(ch(x)))/(x^2 +9))dx

$calculate \int_{0}^{\infty} \frac{\arctan (ch (x))}{x^{2} + 9} dx$

Question Number 103723 Answers: 0 Comments: 0

Solve for n, such that; 1−(1/2)+∙∙∙+(((−1)^n )/(n+1))=∫_0 ^1 (x^(n+1) /(1+x))dx−ln2−(−1)^(n+1)

$Solve for n, such that;$ $1 - \frac{1}{2} + \cdot \cdot \cdot + \frac{{(- 1)}^{n}}{n + 1} = \int_{0}^{1} \frac{x^{n + 1}}{1 + x} dx - \ln 2 - {(- 1)}^{n + 1}$

Question Number 103683 Answers: 1 Comments: 1

∫_0 ^1 tan^(−1) (((2x−1)/(1+x−x^2 )))dx

$\int_{0}^{1} {t a n}^{- 1} (\frac{2 x - 1}{1 + x - x^{2}}) d x$

Question Number 103607 Answers: 1 Comments: 0

what is the value of ∫_c (x+2y)dx+(4−2x)dy around the ellipse C: (x^2 /(16))+(y^2 /8)=1 in the counterclockwise direction ?

$w h a t i s t h e v a l u e o f \int_{c} (x + 2 y) d x + (4 - 2 x) d y$ $a r o u n d t h e e l l i p s e C : \frac{x^{2}}{16} + \frac{y^{2}}{8} = 1$ $i n t h e c o u n t e r c l o c k w i s e$ $d i r e c t i o n ?$

Question Number 103593 Answers: 1 Comments: 0

calculate ∫_(−∞) ^∞ (dx/((x^2 +x +1)^2 (2x^2 +5)^2 ))

$calculate \int_{- \infty}^{\infty} \frac{dx}{{(x^{2} + x + 1)}^{2} {({2 x}^{2} + 5)}^{2}}$

Question Number 103591 Answers: 1 Comments: 4

calculate ∫_3 ^(+∞) (dx/((x^2 −1)^3 (x+2)^2 ))

$calculate \int_{3}^{+ \infty} \frac{dx}{{(x^{2} - 1)}^{3} {(x + 2)}^{2}}$

Question Number 103721 Answers: 2 Comments: 0

∫_0 ^∞ ((cosx)/(x^2 +1))dx

$\int_{0}^{\infty} \frac{c o s x}{x^{2} + 1} d x$

Question Number 103515 Answers: 1 Comments: 0

given f(x) = f(x+(π/6)) ∀x∈R if ∫_0 ^(π/6) f(x)dx = T then ∫_π ^(7π/3) f(x+π) dx ?

$g i v e n f (x) = f (x + \frac{π}{6}) \forall x \in R$ $i f \underset{0}{\int^{π / 6}} f (x) d x = T t h e n \underset{π}{\int^{7 π / 3}} f (x + π)$ $d x ?$

Question Number 103512 Answers: 2 Comments: 2

∫ ((x dx)/((cot x+tan x)^2 )) = (a) (x/(16))−((x sin 4x)/(32))−((cos 4x)/(128))+c (b) (x/(16))+((x sin 4x)/(32))−((cos 4x)/(128))+c (c) (x/(16))+((xsin 4x)/(64))+((cos 4x)/(128))+c (d)(x/(16))+((xcos 4x)/(32))+((sin 4x)/(128))+c

$\int \frac{x d x}{{(\cot x + \tan x)}^{2}} =$ $(a) \frac{x}{16} - \frac{x \sin 4 x}{32} - \frac{\cos 4 x}{128} + c$ $(b) \frac{x}{16} + \frac{x \sin 4 x}{32} - \frac{\cos 4 x}{128} + c$ $(c) \frac{x}{16} + \frac{x \sin 4 x}{64} + \frac{\cos 4 x}{128} + c$ $(d) \frac{x}{16} + \frac{x \cos 4 x}{32} + \frac{\sin 4 x}{128} + c$

Question Number 103511 Answers: 1 Comments: 1

∫ (dx/((√x) ((x)^(1/4) +1))) =__ (a) −((9 (x)^(1/4) +1)/(18((x)^(1/4) +1)^9 )) + c (b) ((9 (x)^(1/4) +1)/(18((x)^(1/4) +1)^9 )) +c (c) −((9 (x)^(1/4) −1)/(18((x)^(1/4) +1)^9 )) +c (d) ((9 (x)^(1/4) +1)/(8((x)^(1/4) +1)^9 )) + c

$\int \frac{d x}{\sqrt{x} (\sqrt[4]{x} + 1)} =__$ $(a) - \frac{9 \sqrt[4]{x} + 1}{18 {(\sqrt[4]{x} + 1)}^{9}} + c$ $(b) \frac{9 \sqrt[4]{x} + 1}{18 {(\sqrt[4]{x} + 1)}^{9}} + c$ $(c) - \frac{9 \sqrt[4]{x} - 1}{18 {(\sqrt[4]{x} + 1)}^{9}} + c$ $(d) \frac{9 \sqrt[4]{x} + 1}{8 {(\sqrt[4]{x} + 1)}^{9}} + c$

Question Number 103537 Answers: 1 Comments: 0

∫(x/((a^2 cosx+b^2 sinx)))dx

$\int \frac{x}{(a^{2} cosx + b^{2} sinx)} dx$

Question Number 103454 Answers: 1 Comments: 0

∫ (x^2 +2x^4 +3x^6 )(√(1+x^2 +x^4 )) dx

$\int (x^{2} + 2 x^{4} + 3 x^{6}) \sqrt{1 + x^{2} + x^{4}} d x$

Question Number 103397 Answers: 1 Comments: 0

I(n)=∫_0 ^∞ ((ln x)/(cosh^n x ))dx is there a simpler way to calculat those values

$I (n) = \int_{0}^{\infty} \frac{\ln x}{\cosh^{n} x} d x$ $i s t h e r e a s i m p l e r w a y t o$ $c a l c u l a t t h o s e v a l u e s$

Question Number 103343 Answers: 1 Comments: 0

∫_0 ^1 x^(−x) dx

$\int_{0}^{1} x^{- x} d x$

Question Number 103312 Answers: 4 Comments: 0

∫_0 ^∞ (1/((1+x^2 )^6 )) dx ?

$\underset{0}{\int^{\infty}} \frac{1}{{(1 + x^{2})}^{6}} d x ?$

Question Number 103241 Answers: 0 Comments: 0

∫x^(−x) dx

$\int x^{- x} d x$

Question Number 103220 Answers: 1 Comments: 0

∫_0 ^∞ (x^3 /(e^x +1))dx

$\int_{0}^{\infty} \frac{x^{3}}{e^{x} + 1} d x$

Question Number 103198 Answers: 4 Comments: 1

∫_0 ^1 sin(logx)dx

$\int_{0}^{1} s i n (l o g x) d x$

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