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IntegrationQuestion and Answers: Page 149

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

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

Question Number 103196 Answers: 1 Comments: 0

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

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

Question Number 103154 Answers: 2 Comments: 0

∫_0 ^1 logxlog(1−x)dx

$\int_{0}^{1} l o g x l o g (1 - x) d x$

Question Number 103089 Answers: 1 Comments: 0

solve: (sin^2 (x)−y)dx−tan(x)dy=0

$s o l v e :$ $({s i n}^{2} (x) - y) d x - t a n (x) d y = 0$

Question Number 103080 Answers: 0 Comments: 0

calculate A_n =∫_0 ^∞ ((cos(nx))/((1+x^2 )^n ))dx with n integr natural

$c a l c u l a t e A_{n} = \int_{0}^{\infty} \frac{c o s (n x)}{{(1 + x^{2})}^{n}} d x$ $w i t h n i n t e g r n a t u r a l$

Question Number 103078 Answers: 0 Comments: 0

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

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

Question Number 103077 Answers: 0 Comments: 0

find ∫_0 ^∞ ((x^2 cosx)/((x^2 +x+2)^2 ))dx

$f i n d \int_{0}^{\infty} \frac{x^{2} c o s x}{{(x^{2} + x + 2)}^{2}} d x$

Question Number 103040 Answers: 5 Comments: 0

given 5x+12y = 60 min value of (√(x^2 +y^2 ))

$g i v e n 5 x + 12 y = 60$ $m i n v a l u e o f \sqrt{x^{2} + y^{2}}$

Question Number 102987 Answers: 2 Comments: 0

lim_(x→0) ((x^2 sin (x^(−4) ))/x) ?

$\lim_{x \to 0} \frac{x^{2} \sin (x^{- 4})}{x} ?$

Question Number 102926 Answers: 3 Comments: 0

∫ (dθ/(2sin^2 θ−cos^2 θ)) ?

$\int \frac{d θ}{2 {s i n}^{2} θ - {c o s}^{2} θ} ?$

Question Number 102922 Answers: 1 Comments: 1

∫ (dx/(x^3 +3x−5)) ?

$\int \frac{d x}{x^{3} + 3 x - 5} ?$

Question Number 103071 Answers: 0 Comments: 0

∫(e^x /((1+x^2 )^2 ))∙(x^3 −x^2 +x+1)dx

$\int \frac{e^{x}}{{(1 + x^{2})}^{2}} \cdot (x^{3} - x^{2} + x + 1) dx$

Question Number 102911 Answers: 2 Comments: 1

∫ ((sin(x))/x) dx

$\int \frac{\sin (x)}{x} dx$

Question Number 102905 Answers: 1 Comments: 0

I=2∫_0 ^(1/(√2)) ((sin^(−1) (x))/x) dx −∫_0 ^1 ((tan^(−1) (x))/x)dx

$I = 2 \underset{0}{\int^{\frac{1}{\sqrt{2}}}} \frac{\sin^{- 1} (x)}{x} d x - \underset{0}{\int^{1}} \frac{\tan^{- 1} (x)}{x} d x$

Question Number 102790 Answers: 1 Comments: 0

I=2∫_0 ^(1/(√2)) ((sin^(−1) (x))/x) dx −∫_0 ^1 ((tan^(−1) (x))/x) dx

$I = 2 \underset{0}{\int^{\frac{1}{\sqrt{2}}}} \frac{\sin^{- 1} (x)}{x} d x - \underset{0}{\int^{1}} \frac{\tan^{- 1} (x)}{x} d x$

Question Number 102894 Answers: 3 Comments: 0

∫ (√(x+(√(x+(√(x+(√(x+(√(x+...)))))))))) dx

$\int \sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x + . . .}}}}} dx$

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