Question
Evaluate the integral
2ln(c)c2x+C,C∈R
Evaluate
∫c2xdx
Use the substitution dx=21dt to transform the integral
More Steps

Evaluate
t=2x
Calculate the derivative
dt=2dx
Evaluate
dx=21dt
∫c2x×21dt
Simplify
∫2c2xdt
Use the substitution t=2x to transform the integral
∫2ctdt
Rewrite the expression
∫21ctdt
Use the property of integral ∫kf(x)dx=k∫f(x)dx
21×∫ctdt
Use the property of integral ∫axdx=lnaax
21×ln(c)ct
Multiply the terms
2ln(c)ct
Substitute back
2ln(c)c2x
Solution
2ln(c)c2x+C,C∈R
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