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IntegrationQuestion and Answers: Page 60

Question Number 156224 Answers: 0 Comments: 1

∫_0 ^( 1) (1/( (√(ln(x^2 )+1)) )) dx

$\int_{0}^{1} \frac{1}{\sqrt{\ln (x^{2}) + 1}} d x$

Question Number 156222 Answers: 0 Comments: 1

∫_0 ^( 1) ln((sin(x)cos(x))^2 +1) dx

$\int_{0}^{1} \ln ({(\sin (x) \cos (x))}^{2} + 1) d x$

Question Number 156218 Answers: 1 Comments: 4

∫_0 ^( 1) (1/( (√(x(√(x^2 (√(x^3 (√(x^4 +1)))))))) )) dx

$\int_{0}^{1} \frac{1}{\sqrt{x \sqrt{x^{2} \sqrt{x^{3} \sqrt{x^{4} + 1}}}}} d x$

Question Number 156194 Answers: 0 Comments: 1

∫_0 ^( 1) (√(x(√(x^2 (√(x^3 .....(√x^n ))))))) dx n ∈ N

$\int_{0}^{1} \sqrt{x \sqrt{x^{2} \sqrt{x^{3} . . . . . \sqrt{x^{n}}}}} d x$ $n \in N$

Question Number 156177 Answers: 1 Comments: 0

∫_(−∞) ^∞ ((sin (x))/(x^2 +x+1))dx=?

$\int_{- \infty}^{\infty} \frac{\sin (x)}{x^{2} + x + 1} d x = ?$

Question Number 156182 Answers: 1 Comments: 0

Question Number 156028 Answers: 1 Comments: 0

Ω := ∫_0 ^( (π/2)) (√(sin(x))) ln(sin( x ))dx=? m.n..

$Ω := \int_{0}^{\frac{π}{2}} \sqrt{s i n (x)} \ln (s i n (x)) d x = ?$ $m . n . .$

Question Number 156009 Answers: 0 Comments: 5

Please calculate 1). ∫sin^5 x dx 2). ∫cos^2 x dx 3). ∫tan^3 x.sec^5 x dx 4). ∫cos 5x.cos 3x dx 5). ∫ ((tan^2 x−1)/(sec^2 x)) dx

$Please calculate$ $1) . \int \sin^{5} x dx$ $2) . \int \cos^{2} x dx$ $3) . \int \tan^{3} x . \sec^{5} x dx$ $4) . \int \cos 5 x . \cos 3 x dx$ $5) . \int \frac{\tan^{2} x - 1}{\sec^{2} x} dx$

Question Number 156008 Answers: 0 Comments: 8

Tekhnic Integration by part 1) Find ∫x.sec^2 x dx 2) Find ∫x.e^(2x) dx 3) Find ∫ln x dx 4) Find ∫x^2 .e^(2x) dx 5) Find ∫e^x cos x dx

$Tekhnic Integration by part$ $1) Find \int x . \sec^{2} x dx$ $2) Find \int x . e^{2 x} dx$ $3) Find \int \ln x dx$ $4) Find \int x^{2} . e^{2 x} dx$ $5) Find \int e^{x} \cos x dx$

Question Number 155986 Answers: 0 Comments: 0

Question Number 155933 Answers: 0 Comments: 1

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

$\int_{- \infty}^{\infty} \frac{\sqrt{1 + \frac{1}{x^{2} + 1}}}{x^{2} + x + 1} d x$

Question Number 155930 Answers: 1 Comments: 2

∫_0 ^( 1) ((sin(x)cos(x))/(sin^3 (x)+cos^3 (x))) dx

$\int_{0}^{1} \frac{\sin (x) \cos (x)}{\sin^{3} (x) + \cos^{3} (x)} d x$

Question Number 155929 Answers: 0 Comments: 0

∫_1 ^( 2) ((√x^2 )/(ln(x^2 ))) dx

$\int_{1}^{2} \frac{\sqrt{x^{2}}}{\ln (x^{2})} d x$

Question Number 155919 Answers: 1 Comments: 0

Question Number 159717 Answers: 0 Comments: 0

Question Number 155897 Answers: 1 Comments: 0

∫ x(arctan x)^2 dx=?

$\int x {(\arctan x)}^{2} dx = ?$

Question Number 155883 Answers: 0 Comments: 1

∫ ((tan^2 x)/(1−tan^2 x)) dx=?

$\int \frac{\tan^{2} x}{1 - \tan^{2} x} d x = ?$

Question Number 155863 Answers: 0 Comments: 2

monster integral ∫_0 ^( (π/4)) ln^2 (sin(2x)+ cos(3x)) dx

$\underset{―}{monster integral}$ $\int_{0}^{\frac{π}{4}} \ln^{2} (\sin (2 x) + \cos (3 x)) d x$

Question Number 156775 Answers: 1 Comments: 1

f is a function that assigns to each natural number multiplication of its digits for exampl : f( 200)=0 f ( 128 )=1×2×8 =16 find the value of : f (100) + f(101 )+ f (102 )+...f(999)=?

$f i s a f u n c t i o n t h a t a s s i g n s$ $t o e a c h n a t u r a l n u m b e r$ $m u l t i p l i c a t i o n o f i t s d i g i t s$ $f o r e x a m p l : f (200) = 0$ $f (128) = 1 \times 2 \times 8 = 16$ $f i n d t h e v a l u e o f :$ $f (100) + f (101) + f (102) + . . . f (999) = ?$

Question Number 155759 Answers: 0 Comments: 1

∫_0 ^( 1) ln((sin(x)+cos(x))^2 +1) dx

$\int_{0}^{1} \ln ({(\sin (x) + \cos (x))}^{2} + 1) d x$

Question Number 155686 Answers: 2 Comments: 0

∫_0 ^(π/2) (dx/(1+tan x)) =?

$\int_{0}^{π / 2} \frac{d x}{1 + \tan x} = ?$

Question Number 155674 Answers: 0 Comments: 0

monster integral ∫_0 ^( (π/4)) ln^2 (sin(2x)+ cos(3x)) dx

$\underset{―}{monster integral}$ $\int_{0}^{\frac{π}{4}} \ln^{2} (\sin (2 x) + \cos (3 x)) d x$

Question Number 155553 Answers: 0 Comments: 0

∫_(−∞) ^( ∞) ((sin(x^2 )cos(x^3 ))/((ln((sin(x)cos(x))^2 ))^2 +1)) dx

$\int_{- \infty}^{\infty} \frac{\sin (x^{2}) \cos (x^{3})}{{(\ln ({(\sin (x) \cos (x))}^{2}))}^{2} + 1} d x$

Question Number 155533 Answers: 1 Comments: 0

coefficiient of x^( 60) = ? P = (x−1)(x^( 2) −1)(x^( 3) −1)...(x^( 15) −1)

$c o e f f i c i i e n t o f x^{60} = ?$ $P = (x - 1) (x^{2} - 1) (x^{3} - 1) . . . (x^{15} - 1)$

Question Number 155252 Answers: 1 Comments: 0

∫_0 ^( (π/2)) x.sin^( 2) (x).ln(sin(x))dx

$\int_{0}^{\frac{π}{2}} x . {s i n}^{2} (x) . l n (s i n (x)) d x$

Question Number 155217 Answers: 0 Comments: 0

∫_(−∞) ^( ∞) ((ln((√(x^4 +1))))/( (√(x^4 +1)))) dx

$\int_{- \infty}^{\infty} \frac{\ln (\sqrt{x^{4} + 1})}{\sqrt{x^{4} + 1}} d x$

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