Gustavo

[Gustavo @iltedesco22]

@hypergeriruru07 (1/√3)*arctan(x/√3) [0,1]
(1/√3)*[arctan(1/√3)-arctan(0/√3)]
(√(3)/3)*[π/6]=(√(3)/18)*π

[Gustavo @iltedesco22]

@IQTestBrain lnx=2,303logx
logx=u
lnx=2,303.u
(2,303.u)¹ᐟᵘ=(2,303.u)ᵘ
1/u=u; u²=1; u=1; u=-1
If u=1; x=10
if u=-1; x=1/10
x=

[Gustavo @iltedesco22]

@leetutarea 2(1-ln2)

[Gustavo @iltedesco22]

@Sam_Axiom 2ˣ=u
√(2u)=1
2u=1; u=½
2ˣ=½; 2ˣ=2⁻¹; x=-1

[Gustavo @iltedesco22]

@mathsrick_ x=8
y=2

[Gustavo @iltedesco22]

Vozinha, el shortstop de Cabo Verde
#MUNDIALXTELEVEN

[Gustavo @iltedesco22]

@Diarytells u=√(1+lnx)
2∫du=2u+c=2√(1+lnx)+c

[Gustavo @iltedesco22]

@sonukg4india f(x)=√(r²-(x-h)²)
f'(x)=-(x-h)/√(r²-(x-h)²)
f'(1)+f'(7)=0
-(1-h)/√(r²-(1-h)²)+...
...(-(7-h)/√(r²-(7-h)²))=0
h=(1+7)/2=4
r=h-0=4-0=4
f(2)=√(16-(-2)²)=√(16-4)=√12
f(2)=√12=2√3

[Gustavo @iltedesco22]

@ZahlenRMD ∫dx/x√(1+x²)²)
x²=tanθ; 2xdx=sec²θdθ
½∫cscθdθ=½ln(cscθ-cotθ)+c
cscθ=√(1+x⁴)/x²; cotθ=1/x²
½ln(√(1+x⁴)-1)-lnx +c

[Gustavo @iltedesco22]

@sonukg4india √(lnx).lnx=8lne
√(lnx).lnx=8
ln³x=4³; lnx=4; x=e⁴
x¹ᐟ⁴=((e)⁴)¹ᐟ⁴=e

[Gustavo @iltedesco22]

@hypergeriruru07 By parts: ∫udv=uv-∫vdu
u=ln(2+x)
du=dx/(2+x)
v=∫xdx=½x²
½x²ln(2+x)-½∫x²dx/(2+x)
½x²ln(2+x)-½∫xdx+∫dx-2∫dx/2+x
½x²ln(2+x)-¼x²+x-2ln(2+x) [0,1]
½ln3-¼+1-2ln3+2ln2
½ln3+¾-2ln3+2ln2
2ln2-(3/2)ln3+¾ s.u.

[Gustavo @iltedesco22]

@MDiener72345 Frauen

[Gustavo @iltedesco22]

@Diarytells I=∫xsinxdx/(1+cos²x)
I=π∫sinxdx/(1+cos²x)-...
...∫xsinxdx/(1+cos²x)
2i=I+I
2I=π∫sinxdx/(1+cos²x)
I=(-½)*π*arctan (cosx) [0,π]
I=-½*π(-¼π-¼π)=-½π(-½π)
I=¼*π² s.u.

[Gustavo @iltedesco22]

@GermanSimply_ Guten Morgen

[Gustavo @iltedesco22]

@xxChessMaster 1.Qg5, if...1.f6; 2.Qxg6++
if...1.e6 ; 2.Qd8++
if...1.a5; 2.Qb5++

[Gustavo @iltedesco22]

@pickover xlnx=½√xlnx
2x=√x; 2√x=1; √x=½; x=¼
x=¼

[Gustavo @iltedesco22]

@sonukg4india lnx=(½√x)lnx
√x=2; x=4

[Gustavo @iltedesco22]

@Diarytells @sonukg4india ∫cos⁸x.cosxdx=∫(cos²x)⁴.cosxdx
∫(1-sin²x)⁴.cosxdx
t=sinx; dt=cosx
x=0; t=0;x=π/2; t=1
∫(1-t²)⁴dt [0,1]
∫t⁸dt-4∫t⁶dt+6∫t⁴dt-4∫t²dt+∫dt
⅑t⁹-(4/7)t⁷+(6/5)t⁵-(4/3)t³+t [0,1]
(1/9)-(4/7)+(6/5)-(4/3)+1
(35-180+378-420+315)/315
128/315 s u.

[Gustavo @iltedesco22]

@Afghan_Engineer a)i=i1+i2
b)i1=i+i3
1) 2=30*i1
i1=1/15 A
2) 15i+15i2=2
From a) i-i2=1/15 ; 15i-15i2=1
c)15i+15i2=2
d)15i-15i2=1
30i=3; i=3/30=1/10 A=100mA
i=100 mA

[Gustavo @iltedesco22]

@Afghan_Engineer V1=V2=V3=3*2=6v
i3=6v/(1+5)=1A
P5=I²*R=(1)²*5=5w