2x6 + 4x5 + x4 + 11x3 + 2x2 + 4x + 4
Answer:
½ sec²(x) + ln(|cos(x)|) + C
Step-by-step explanation:
∫ tan³(x) dx
∫ tan²(x) tan(x) dx
∫ (sec²(x) − 1) tan(x) dx
∫ (sec²(x) tan(x) − tan(x)) dx
∫ sec²(x) tan(x) dx − ∫ tan(x) dx
For the first integral, if u = sec(x), then du = sec(x) tan(x) dx.
∫ u du = ½ u² + C
Substituting back:
½ sec²(x) + C
For the second integral, tan(x) = sin(x) / cos(x). If u = cos(x), then du = -sin(x) dx.
∫ -du / u = -ln(u) + C
Substituting back:
-ln(|cos(x)|) + C
Therefore, the total integral is:
½ sec²(x) + ln(|cos(x)|) + C
Hello :)
In 8 years, the father will be 2 times older than the child.
In 8 years, the father will be 40
In 8 years, the child will be 20
40 ÷ 20 = 2
So again, the answer is 8 years :)
Hope this helps and have a great day
Answer:
see below
Step-by-step explanation:
The x intercepts are where it crosses the x axis
( -4,0)
The y intercepts are where it crosses the y axis
( 0, 4)
Answer:
-5y + 8x
Step-by-step explanation:
