Пошаговое объяснение:
1)
\begin{gathered}\int\limits {(3x+1)^{\frac{2}{3} }} \, dx =\frac{1}{3}\int\limits {t}^{\frac{2}{3} } \, dt=\\=\frac{1}{3}*\frac{t^{\frac{2}{3} +1}}{\frac{2}{3} +1}= \frac{1}{3}* \frac{3}{5}t^{\frac{5}{3}}=\frac{1}{5}*(3x+1)^{\frac{5}{3}}\\3x+1=t; 3dx=dt; \\dx=\frac{1}{3}dt\end{gathered}
∫(3x+1)
3
2
dx=
3
1
∫t
3
2
dt=
=
3
1
∗
3
2
+1
t
3
2
+1
=
3
1
∗
5
3
t
3
5
=
5
1
∗(3x+1)
3
5
3x+1=t;3dx=dt;
dx=
3
1
dt
2)\int \frac{dx}{xln^2x}=\int \frac{d(lnx)}{ln^2x}=\int \frac{dt}{t^2}=-\frac{1}{t}=-\frac{1}{lnx}∫
xln
2
x
dx
=∫
ln
2
x
d(lnx)
=∫
t
2
dt
=−
t
1
=−
lnx
1
Пошаговое объяснение:
1) 4х=24+х
4x - x=24
3x=24
x=8
2) 8х-8=20-6х
8x + 6x = 20 + 8
14x = 28
x=2
3) 5/6х+16=4/9х+9
5/6х+16=4/9х+9 умножаем обе части на 18
15x + 288 = 8x +162
15x – 8x = 162 - 288 7
x = -126 x = -18
4 ) 4*(х-3)=х+6
4x – 12 = x +6
4x – x = 6+12
3x = 18
x= 6
5) 4-6*(х+2)=3 - 5х
4 + 6x -12 = 3 – 5x
6x +5x = 3 – 4 + 12
11x=11
x=1
6) 5/6*(1/3х-1/5)=3х+3 1/3
5x/18 – 1/6 = 3x+10/3
5x-3 = 54x+60
-49x = 63
x= - 63/49
x= - 9/7
7) 4*(х-1)=2*(2х-8)+12
4x-4=4x-16+12
4x-4x = -16+12+4
x=0
8) 7*(4х-1)=6-2*(3-14х)
28x – 7 = 6 – 6 + 28x
28x – 28x = 6-6+7
x= 7
