Question and Answers Forum

1) find f(a) =∫_0 ^∞ (dx/(x^4 +a)) with a>0 2) find g(a)=∫_0 ^∞ (dx/((x^4 +a)^2 )) 3) find value of integrals ∫_0 ^∞ (dx/(x^4 +1)) ,∫_0 ^∞ (dx/(2x^4 +8)) ∫_0 ^∞ (dx/((x^4 +1)^2 )) and ∫_0 ^∞ (dx/((2x^4 +8)^2 ))

$1) f i n d f (a) = \int_{0}^{\infty} \frac{d x}{x^{4} + a} w i t h a > 0$ $2) f i n d g (a) = \int_{0}^{\infty} \frac{d x}{{(x^{4} + a)}^{2}}$ $3) f i n d v a l u e o f i n t e g r a l s \int_{0}^{\infty} \frac{d x}{x^{4} + 1}, \int_{0}^{\infty} \frac{d x}{2 x^{4} + 8}$ $\int_{0}^{\infty} \frac{d x}{{(x^{4} + 1)}^{2}} a n d \int_{0}^{\infty} \frac{d x}{{(2 x^{4} + 8)}^{2}}$

Question Number 85158 Answers: 0 Comments: 0

calculate U_n = ∫_(−(1/n)) ^(1/n) x^2 (√((1−x)/(1+x)))dx (n integr and n≥2) 2) find nature of Σ U_n

$c a l c u l a t e U_{n} = \int_{- \frac{1}{n}}^{\frac{1}{n}} x^{2} \sqrt{\frac{1 - x}{1 + x}} d x (n i n t e g r a n d n ⩾ 2)$ $2) f i n d n a t u r e o f Σ U_{n}$

Question Number 85148 Answers: 0 Comments: 0

∫_0 ^1 ((1+x^4 )/(1+x^3 +x^7 )) dx

$\int_{0}^{1} \frac{1 + x^{4}}{1 + x^{3} + x^{7}} d x$

Question Number 85097 Answers: 1 Comments: 0

∫_(−π) ^π x^(2020) (sin x+cos x) dx = 8 find ∫_(−π) ^π x^(2020) cos x dx = ?

$\underset{- π}{\int^{π}} x^{2020} (\sin x + \cos x) dx = 8$ $find \underset{- π}{\int^{π}} x^{2020} \cos x dx = ?$

Question Number 85059 Answers: 1 Comments: 0

Question Number 85009 Answers: 1 Comments: 1

calculate ∫_0 ^∞ (x^n /(sh(x)))dx with n integr natural

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

Question Number 84958 Answers: 0 Comments: 0

Question Number 84957 Answers: 0 Comments: 1

∫ (2−x^2 )^3 dx =

$\int {(2 - x^{2})}^{3} dx =$

Question Number 84956 Answers: 1 Comments: 3

show that ∫_0 ^(+∞) (1/(x^4 +2x^2 cos(((2π)/5))+1)) dx=(π/(2φ))

$s h o w t h a t$ $\int_{0}^{+ \infty} \frac{1}{x^{4} + 2 x^{2} c o s (\frac{2 π}{5}) + 1} d x = \frac{π}{2 ϕ}$

Question Number 84942 Answers: 1 Comments: 0

∫_0 ^x sinh(x−t) cosh(t) dt

$\int_{0}^{x} s i n h (x - t) c o s h (t) d t$

Question Number 84894 Answers: 0 Comments: 1

Question Number 84879 Answers: 2 Comments: 1

e^(∫((2dx)/(xlnx)))

$e^{\int \frac{2 dx}{xlnx}}$

Question Number 84859 Answers: 0 Comments: 0

show that lim_(n→∞) ∫_0 ^1 ...∫_0 ^1 (n/(x_1 +x_2 +x_3 +...+x_n ))dx_1 dx_2 ...dx_n =2

$s h o w t h a t$ $\underset{n \to \infty}{l i m} \int_{0}^{1} . . . \int_{0}^{1} \frac{n}{x_{1} + x_{2} + x_{3} + . . . + x_{n}} {d x}_{1} {d x}_{2} . . . {d x}_{n} = 2$

Question Number 84843 Answers: 0 Comments: 2

∫((sin(7x))/(cos(3x))) dx

$\int \frac{s i n (7 x)}{c o s (3 x)} d x$

Question Number 84810 Answers: 0 Comments: 1

∫_0 ^π ln(((1+b cos(x))/(1+a sin(x)))) dx −1<a<b<1

$\int_{0}^{π} l n (\frac{1 + b c o s (x)}{1 + a s i n (x)}) d x$ $- 1 < a < b < 1$

Question Number 84809 Answers: 1 Comments: 1

∫(x/((x^2 +1)^(3/2) arctan(x))) dx

$\int \frac{x}{{(x^{2} + 1)}^{\frac{3}{2}} a r c t a n (x)} d x$

Question Number 84766 Answers: 1 Comments: 2

∫ (dx/((16+9sin x)^2 ))

$\int \frac{dx}{{(16 + 9 \sin x)}^{2}}$

Question Number 84759 Answers: 1 Comments: 0

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

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

Pg 183 Pg 184 Pg 185 Pg 186 Pg 187 Pg 188 Pg 189 Pg 190 Pg 191 Pg 192

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