Hi there!

To find the indefinite integral, we must integrate by parts.
Let "u" be the expression most easily differentiated, and "dv" the remaining expression. Take the derivative of "u" and the integral of "dv":
u = 4x
du = 4
dv = cos(2 - 3x)
v = 1/3sin(2 - 3x)
Write into the format:
∫udv = uv - ∫vdu
Thus, utilize the solved for expressions above:
4x · (-1/3sin(2 - 3x)) -∫ 4(1/3sin(2 - 3x))dx
Simplify:
-4x/3 sin(2 - 3x) - ∫ 4/3sin(2 - 3x)dx
Integrate the integral:
∫4/3(sin(2 - 3x)dx
u = 2 - 3x
du = -3dx ⇒ -1/3du = dx
-1/3∫ 4/3(sin(2 - 3x)dx ⇒ -4/9cos(2 - 3x) + C
Combine:

What we know:
(Also,
)
What we need to solve:
(This is equal to
)
How you have to subtract
with
to get:

Thus, the answer would be:

Answer:
C
Step-by-step explanation:
(2x-3)(4x+5)
=2x(4x+5)-3(4x+5)
=8x^2+10x-12x-15
=8x^2-2x-15
Answer:
= 6
Step-by-step explanation:
in the third step, they did 2 x -12 and got 24. It should’ve been -24 since it was a positive times a negative. It shouldve been
-24 - (-30)
-24 + 30
= 6