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IntegrationQuestion and Answers: Page 59

Question Number 157096 Answers: 1 Comments: 0

∫_0 ^(π/2) xsin(x)ln(sin(x))dx=?

$\int_{0}^{\frac{π}{2}} xsin (x) \ln (\sin (x)) dx = ?$

Question Number 157016 Answers: 1 Comments: 0

f(x)=(1/(1+2^x ))+(1/(1+3^x ))+(1/(4^x +1)) find ∫_1 ^5 f(x)dx+∫_(−5) ^(−1) f(x)dx

$f (x) = \frac{1}{1 + 2^{x}} + \frac{1}{1 + 3^{x}} + \frac{1}{4^{x} + 1}$ $f i n d \int_{1}^{5} f (x) d x + \int_{- 5}^{- 1} f (x) d x$

Question Number 156915 Answers: 1 Comments: 0

Question Number 156914 Answers: 2 Comments: 0

Question Number 156869 Answers: 2 Comments: 0

Question Number 156860 Answers: 1 Comments: 0

∫_0 ^∞ ((x)^(1/n) /(x^3 +x^2 +x+1))dx=?

$\int_{0}^{\infty} \frac{\sqrt[n]{x}}{x^{3} + x^{2} + x + 1} d x = ?$

Question Number 156841 Answers: 1 Comments: 0

Question Number 156849 Answers: 0 Comments: 0

∫_0 ^1 ((ln(e+(1/(1−t))))/( (√t)))dt=?

$\int_{0}^{1} \frac{l n (e + \frac{1}{1 - t})}{\sqrt{t}} d t = ?$

Question Number 156779 Answers: 2 Comments: 0

∫((ln(1+x^2 ))/(1+x^2 ))

$\int \frac{l n (1 + x^{2})}{1 + x^{2}}$

Question Number 156761 Answers: 2 Comments: 0

prove that ∫((a + b sin x)/((b + a sin x)^2 ))dx=((−cos x)/(b + a sin x))

$p r o v e t h a t$ $\int \frac{a + b \sin x}{{(b + a \sin x)}^{2}} d x = \frac{- \cos x}{b + a \sin x}$

Question Number 156743 Answers: 2 Comments: 0

Question Number 156739 Answers: 0 Comments: 1

Question Number 156695 Answers: 1 Comments: 0

∫sin(ln(x))dx=?

$\int s i n (l n (x)) d x = ?$

Question Number 156616 Answers: 2 Comments: 0

∫_0 ^1 ((arcsin(x))/x)dx=?

$\int_{0}^{1} \frac{a r c s i n (x)}{x} d x = ?$

Question Number 156578 Answers: 0 Comments: 0

Question Number 156577 Answers: 0 Comments: 4

Question Number 156529 Answers: 1 Comments: 0

Question Number 156517 Answers: 1 Comments: 0

∫ (dx/(3tan x+cos x)) =?

$\int \frac{dx}{3 \tan x + \cos x} = ?$

Question Number 156470 Answers: 1 Comments: 0

Q=∫_0 ^∞ (x^c /c^x )dx

$Q = \int_{0}^{\infty} \frac{x^{c}}{c^{x}} d x$

Question Number 156363 Answers: 0 Comments: 0

∫_0 ^(π/2) t^(2n) sin^(2n) tdt

$\int_{0}^{\frac{π}{2}} t^{2 n} {s i n}^{2 n} t d t$

Question Number 156319 Answers: 1 Comments: 1

∫ ((36)/((12cos x+5sin x)^2 )) dx=?

$\int \frac{36}{{(12 \cos x + 5 \sin x)}^{2}} dx = ?$

Question Number 156305 Answers: 1 Comments: 0

∫ ((sec^2 (x))/(3sin^2 (x)−1)) dx

$\int \frac{\sec^{2} (x)}{3 \sin^{2} (x) - 1} dx$

Question Number 156257 Answers: 0 Comments: 0

∫ ((xsin^(−1) (x^2 ))/(1−x^4 )) dx=?

$\int \frac{x \sin^{- 1} (x^{2})}{1 - x^{4}} d x = ?$

Question Number 156269 Answers: 0 Comments: 1

Question Number 156229 Answers: 0 Comments: 4

∫_0 ^( (π/4)) ln(sin(2x)+cos(3x)) dx

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

Question Number 156228 Answers: 1 Comments: 0

∫_0 ^( 1) ((log^3 (1−x^2 ))/x^3 ) dx

$\int_{0}^{1} \frac{\log^{3} (1 - x^{2})}{x^{3}} d x$

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