What is the integral of e^{ln(3cos(x))} ?

The integral of e^{ln(3cos(x))} is 3sin(x)+C

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integral of e^{ln(3cos(x))}

\int e^{l n (3 c o s (x))} d x

3 sin (x) + C

Solution steps

\int e^{l n (3 c o s (x))} d x

Apply log rule:

a^{l o g_{a} (b)} = b

= \int 3 cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= 3 sin (x)

Add a constant to the solution

= 3 sin (x) + C

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\int \frac{11}{a x + d} d x

What is the integral of e^{ln(3cos(x))} ?
The integral of e^{ln(3cos(x))} is 3sin(x)+C