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Question Number 154194 Answers: 0 Comments: 1

Question Number 154195 Answers: 3 Comments: 0

∫((x+sinx)/(1+cosx))dx please,help me

$\int \frac{x + s i n x}{1 + c o s x} d x$ $p l e a s e, h e l p m e$

Question Number 154192 Answers: 1 Comments: 0

Ω :=∫_0 ^( 1) (( x.sin(ln(x)))/(1−x))dx method 1 Ω= Im[∫_0 ^( 1) (( x^( i+1) )/(1−x)) dx=Φ] Φ = ∫_0 ^( 1) (( x^( i+1) +x^( i+2) )/(1−x^( 2) ))dx =^(x^( 2) =t) (1/2)∫_0 ^( 1) (( t^( (i/2)) −t^((i+1)/2) )/(1−t))dt = (1/2) { ψ (1 +((i+1)/2))−ψ (1+(i/2))} = (1/2) { (2/(1+i)) + ψ ( ((1+i)/2) )−(2/i)−ψ ((i/2))} = ((−i)/(−1+i)) + (1/2) {ψ (((1+i)/2))−ψ((i/2) )} = −(1/2) +(i/(2 )) +(1/2) {ψ(((1+i)/2))−ψ((i/2))} Ω = Im (Φ )= (1/2) +(1/2) Im(ψ((1/2) +(i/2)))−(1/2) Im((i/2)) = (1/(2 )) { 1 +(π/2) tanh((π/2)) −1−(π/2) coth((π/2))} =(π/4) {((−1)/(sinh((π/2)).cosh((π/2))))}=((−π)/(2 sinh (π ))) ✓

$Ω := \int_{0}^{1} \frac{x . s i n (l n (x))}{1 - x} d x$ $m e t h o d 1$ $Ω = I m [\int_{0}^{1} \frac{x^{i + 1}}{1 - x} d x = Φ]$ $Φ = \int_{0}^{1} \frac{x^{i + 1} + x^{i + 2}}{1 - x^{2}} d x$ $\overset{x^{2} = t}{=} \frac{1}{2} \int_{0}^{1} \frac{t^{\frac{i}{2}} - t^{\frac{i + 1}{2}}}{1 - t} d t$ $= \frac{1}{2} {ψ (1 + \frac{i + 1}{2}) - ψ (1 + \frac{i}{2})}$ $= \frac{1}{2} {\frac{2}{1 + i} + ψ (\frac{1 + i}{2}) - \frac{2}{i} - ψ (\frac{i}{2})}$ $= \frac{- i}{- 1 + i} + \frac{1}{2} {ψ (\frac{1 + i}{2}) - ψ (\frac{i}{2})}$ $= - \frac{1}{2} + \frac{i}{2} + \frac{1}{2} {ψ (\frac{1 + i}{2}) - ψ (\frac{i}{2})}$ $Ω = I m (Φ) = \frac{1}{2} + \frac{1}{2} I m (ψ (\frac{1}{2} + \frac{i}{2})) - \frac{1}{2} I m (\frac{i}{2})$ $= \frac{1}{2} {1 + \frac{π}{2} t a n h (\frac{π}{2}) - 1 - \frac{π}{2} c o t h (\frac{π}{2})}$ $= \frac{π}{4} {\frac{- 1}{s i n h (\frac{π}{2}) . c o s h (\frac{π}{2})}} = \frac{- π}{2 s i n h (π)} ✓$

Question Number 154186 Answers: 1 Comments: 0

Question Number 154177 Answers: 1 Comments: 2

Question Number 154175 Answers: 2 Comments: 1

Question Number 154172 Answers: 0 Comments: 1

Question Number 154148 Answers: 1 Comments: 0

z^4 - ((50)/(2z^4 - 7)) = 14 ⇒ z = ?

$z^{4} - \frac{50}{2 z^{4} - 7} = 14 \Rightarrow z = ?$

Question Number 154143 Answers: 2 Comments: 0

Question Number 154142 Answers: 2 Comments: 0

Question Number 154138 Answers: 1 Comments: 0

Question Number 154133 Answers: 2 Comments: 0

Given f(x)=((x+(√(1+x^2 ))))^(1/3) +((x−(√(1+x^2 ))))^(1/3) Find f^(−1) (x)=?

$Given f (x) = \sqrt[3]{x + \sqrt{1 + x^{2}}} + \sqrt[3]{x - \sqrt{1 + x^{2}}}$ $Find f^{- 1} (x) = ?$

Question Number 154131 Answers: 0 Comments: 1

A long distance runner runs 14km 30°north of east, 7km 60° north of west, 6km 30° south of west, and finally 4km south. Find his final distance and direction relative to the starting point?

Question Number 154200 Answers: 1 Comments: 0

g(((x−1)/(x+1)))=((7x+3)/(x+1)) and f(x^2 −2x+3)=3x^2 −6x+7 find (f+g)(x)=?

$g (\frac{x - 1}{x + 1}) = \frac{7 x + 3}{x + 1} a n d f (x^{2} - 2 x + 3) = 3 x^{2} - 6 x + 7$ $f i n d (f + g) (x) = ?$