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IntegrationQuestion and Answers: Page 28

Question Number 188036 Answers: 1 Comments: 0

∫2^x e^x dx

$\int 2^{x} e^{x} d x$

Question Number 188035 Answers: 1 Comments: 0

solve ∫(x^2 /((a+bx)^2 ))dx

$s o l v e$ $\int \frac{x^{2}}{{(a + b x)}^{2}} d x$

Question Number 188034 Answers: 1 Comments: 0

solve ∫((x^2 +3)/(x^6 (x^2 +1)))dx

$s o l v e$ $\int \frac{x^{2} + 3}{x^{6} (x^{2} + 1)} d x$

Question Number 187993 Answers: 0 Comments: 0

prove that ∫_0 ^(π/2) ∫_0 ^(π/2) (((sin3x)/(sin2y)))^(1/3) dxdy=(π/(2(√3)))

$p r o v e t h a t$ $\int_{0}^{\frac{π}{2}} \int_{0}^{\frac{π}{2}} \sqrt[3]{\frac{s i n 3 x}{s i n 2 y}} d x d y = \frac{π}{2 \sqrt{3}}$

Question Number 187898 Answers: 2 Comments: 0

∫ ((1−cos x)/(cos x+sin x−1)) dx=?

$\int \frac{1 - \cos x}{\cos x + \sin x - 1} dx = ?$

Question Number 187890 Answers: 1 Comments: 0

Question Number 187855 Answers: 2 Comments: 0

solve ∫((x^4 +x^2 +1)/(2(x^2 +1)))dx

$s o l v e$ $\int \frac{x^{4} + x^{2} + 1}{2 (x^{2} + 1)} d x$

Question Number 187703 Answers: 2 Comments: 0

∫ (1/(5x^2 − 2x − 4)) dx

$\int \frac{1}{{5 x}^{2} - 2 x - 4} dx$

Question Number 187700 Answers: 0 Comments: 1

Find minimum area of the part y=x^2 and y=kx(x^2 −k), k>0

$F i n d m i n i m u m a r e a o f t h e p a r t$ $y = x^{2} a n d y = k x (x^{2} - k), k > 0$

Question Number 187602 Answers: 1 Comments: 0

∫_(1/4) ^(1/2) ((sin^(−1) ((√x))−cos^(−1) ((√x)))/(sin^(−1) ((√x))+cos^(−1) ((√x)))) dx=?

$\underset{1 / 4}{\int^{1 / 2}} \frac{\sin^{- 1} (\sqrt{x}) - \cos^{- 1} (\sqrt{x})}{\sin^{- 1} (\sqrt{x}) + \cos^{- 1} (\sqrt{x})} d x = ?$

Question Number 187531 Answers: 3 Comments: 0

∫_0 ^∞ x^2 e^(−x) dx=?

$\underset{0}{\int^{\infty}} x^{2} e^{- x} d x = ?$

Question Number 187530 Answers: 1 Comments: 0

∫(dx/( (√(a^2 +be^(cx) ))))=?

$\int \frac{d x}{\sqrt{a^{2} + {b e}^{c x}}} = ?$

Question Number 187529 Answers: 1 Comments: 0

∫x^2 ∙sin^(−1) (x)dx=?

$\int x^{2} \cdot {s i n}^{- 1} (x) d x = ?$

Question Number 187528 Answers: 1 Comments: 0

∫_((9π)/2) ^((7π)/(1.5)) (dx/( (√(1−sinx))))=?

$\underset{\frac{9 π}{2}}{\int^{\frac{7 π}{1.5}}} \frac{d x}{\sqrt{1 - s i n x}} = ?$

Question Number 187526 Answers: 2 Comments: 0

∫(dx/(cscx−1))=?

$\int \frac{d x}{c s c x - 1} = ?$

Question Number 187374 Answers: 0 Comments: 2

∫(√((t+1)/(t(k−t))))dt=?

$\int \sqrt{\frac{t + 1}{t (k - t)}} d t = ?$

Question Number 187317 Answers: 2 Comments: 0

∫(dx/(x(√(1−2x))))

$\int \frac{d x}{x \sqrt{1 - 2 x}}$

Question Number 187251 Answers: 0 Comments: 1

∫ ((cos 9x)/(cos 4x. cos 2x)) dx=?

$\int \frac{\cos 9 x}{\cos 4 x . \cos 2 x} d x = ?$

Question Number 187164 Answers: 1 Comments: 0

Question Number 187135 Answers: 1 Comments: 0

∫_( 0) ^( π/4) ((tan^2 x)/(1+sin x)) dx =?

$\underset{0}{\int^{π / 4}} \frac{\tan^{2} x}{1 + \sin x} d x = ?$

Question Number 187095 Answers: 2 Comments: 1

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

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

Question Number 187050 Answers: 0 Comments: 1

∫^(𝛑/4) _0 ((cos^(−1) x + cos x)/(Ln x)) dx =??

${\int_{0}}^{\frac{π}{4}} \frac{{c o s}^{- 1} x + c o s x}{L n x} d x = ? ?$

Question Number 186921 Answers: 0 Comments: 0

Question Number 186911 Answers: 1 Comments: 0

∫_0 ^∞ (1/(1+a^x +a^(x/2) ))dx = (1/(ln a))[ln 3−(π/(3(√3)))]

$\int_{0}^{\infty} \frac{1}{1 + a^{x} + a^{\frac{x}{2}}} d x = \frac{1}{\ln a} [\ln 3 - \frac{π}{3 \sqrt{3}}]$

Question Number 186910 Answers: 1 Comments: 0

∫_0 ^a (√((cos 2x−cos 2a)/(cos 2x+1))) dx=(π/2)(1−cos a)

$\int_{0}^{a} \sqrt{\frac{\cos 2 x - \cos 2 a}{\cos 2 x + 1}} d x = \frac{π}{2} (1 - \cos a)$

Question Number 186973 Answers: 0 Comments: 1

∫5x

$\int 5 x$

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