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IntegrationQuestion and Answers: Page 50

Question Number 161839 Answers: 3 Comments: 0

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

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

Question Number 161830 Answers: 1 Comments: 0

∫(dx/( (√(1−x^(14) ))))

$\int \frac{d x}{\sqrt{1 - x^{14}}}$

Question Number 161773 Answers: 3 Comments: 1

Question Number 161706 Answers: 1 Comments: 0

J =∫_0 ^( 1) (( 1−x)/(( 1+x +x^( 2) + x^( 3) )ln(x))) dx=?

$J = \int_{0}^{1} \frac{1 - x}{(1 + x + x^{2} + x^{3}) l n (x)} d x = ?$

Question Number 161660 Answers: 3 Comments: 0

∫_0 ^(π/4) ln(1+(√2)cos(x))dx=???

$\int_{0}^{\frac{π}{4}} l n (1 + \sqrt{2} c o s (x)) d x = ? ? ?$

Question Number 161656 Answers: 1 Comments: 3

∫_0 ^1 ((xln(1+x))/(1+x^2 ))dx

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

Question Number 161652 Answers: 0 Comments: 0

∫_0 ^( 1) ((xlog(a+x))/(1+x^2 ))dx ∀ ∣a∣ ∈ N

$\int_{0}^{1} \frac{xlog (a + x)}{1 + x^{2}} dx \forall ∣ a ∣ \in N$

Question Number 161703 Answers: 2 Comments: 1

(1)∫ ((sin x−cos x)/( (√(sin 2x)))) dx (2) ∫_0 ^( π/2) cos 7x cos 17x cos 37x dx

$(1) \int \frac{\sin x - \cos x}{\sqrt{\sin 2 x}} d x$ $(2) \int_{0}^{π / 2} \cos 7 x \cos 17 x \cos 37 x d x$

Question Number 161646 Answers: 0 Comments: 0

Question Number 161609 Answers: 0 Comments: 0

∫_0 ^1 ((xln(1+x^4 ))/(1+x^2 ))dx=?

$\int_{0}^{1} \frac{x l n (1 + x^{4})}{1 + x^{2}} d x = ?$

Question Number 161537 Answers: 2 Comments: 0

∫_0 ^( (π/4)) ((1+tan^4 (x))/(cot^2 (x))) dx =?

$\int_{0}^{\frac{π}{4}} \frac{1 + \tan^{4} (x)}{\cot^{2} (x)} d x = ?$

Question Number 161443 Answers: 1 Comments: 0

Question Number 161412 Answers: 0 Comments: 0

Question Number 161407 Answers: 1 Comments: 0

Question Number 161404 Answers: 1 Comments: 0

Question Number 161393 Answers: 0 Comments: 0

Question Number 161329 Answers: 0 Comments: 0

∫_1 ^( 2) ((tan^(−1) (x−1)log(x))/x)dx

$\int_{1}^{2} \frac{\tan^{- 1} (x - 1) \log (x)}{x} dx$

Question Number 161285 Answers: 5 Comments: 0

(1) ∫ (dx/(1−2cos x)) (2) ∫ ((sin 2x)/(sin x−sin^2 2x)) dx (3) ∫ (dx/(cos 2x−sin x))

$(1) \int \frac{d x}{1 - 2 \cos x}$ $(2) \int \frac{\sin 2 x}{\sin x - \sin^{2} 2 x} d x$ $(3) \int \frac{d x}{\cos 2 x - \sin x}$

Question Number 161281 Answers: 0 Comments: 0

Question Number 161265 Answers: 1 Comments: 2

Question Number 161256 Answers: 1 Comments: 0

Given f(x)=f(x+2), ∀x∈R If ∫_0 ^2 f(x)dx= p then ∫_0 ^(2020) f(x+2a)dx=? for a∈Z^+

$G i v e n f (x) = f (x + 2), \forall x \in R$ $I f \underset{0}{\int^{2}} f (x) d x = p t h e n \underset{0}{\int^{2020}} f (x + 2 a) d x = ?$ $f o r a \in Z^{+}$

Question Number 161233 Answers: 0 Comments: 0

Question Number 161229 Answers: 1 Comments: 0

Given f(x)= { ((1−∣x∣ ; x≤1)),((∣x∣−1 ; x>1)) :} find ∫_(−3) ^( 8) [f(x−1)+f(x+1)] dx.

$G i v e n f (x) = {\begin{cases} 1 - ∣ x ∣; x ⩽ 1 \\ ∣ x ∣ - 1; x > 1 \end{cases}$ $f i n d \int_{- 3}^{8} [f (x - 1) + f (x + 1)] d x .$

Question Number 161212 Answers: 2 Comments: 2

∫_( 0) ^( (π/2)) ((x sin x cos x)/(cos^4 x +sin^4 x)) dx =?

$\int_{0}^{\frac{π}{2}} \frac{x \sin x \cos x}{\cos^{4} x + \sin^{4} x} d x = ?$

Question Number 161178 Answers: 1 Comments: 0

∫^∞ _2 ((arctg(x))/(arctg((x/2))))dx=???

${\int_{2}}^{\infty} \frac{a r c t g (x)}{a r c t g (\frac{x}{2})} d x = ? ? ?$

Question Number 161176 Answers: 0 Comments: 0

calculate Θ := Σ_(n=1) ^∞ (( (−1 )^( n−1) )/(n ( n + (1/3) ))) =? ■ m.n −−−−−−−−−−−−−

$c a l c u l a t e$ $Θ := \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n - 1}}{n (n + \frac{1}{3})} = ? ◼ m . n$ $- - - - - - - - - - - - -$

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