1003107807 | math4u.vsb.cz

SubArea:

Primitive function

Level:

Project ID:

1003107807

Accepted:

1

Find a function

F (x)

, that is primitive to the function

f (x) = 2^{x} \cdot \ln 2 + 4^{x} \cdot 2 \ln 2 + 8^{x} \cdot 3 \ln 2

on

R

, and satisfies the condition

F (0) = 5

.

F (x) = 2^{x} + 4^{x} + 8^{x} + 2

F (x) = \frac{2^{x}}{\ln 2} + \frac{4^{x}}{\ln 4} + \frac{8^{x}}{\ln 8} + 2 x

F (x) = 2^{x} + 4^{x} + 8^{x} + 5

F (x) = 2^{x} \cdot \ln 2 + 2^{x + 1} \cdot \ln 2 + 2^{x + 3} \cdot \ln 2 + 5