Integral of tan(ln(x))/x (substitution)

Описание к видео Integral of tan(ln(x))/x (substitution)

Integral of tan(ln(x))/x (substitution)```
To solve the integral ∫tan(ln(x)) / x dx using substitution:

Step 1: Substitution
Let u = ln(x), so du/dx = 1/x, or dx = x du.

Step 2: Rewrite the Integral
Substitute u and dx into the integral:
∫tan(ln(x)) / x dx = ∫tan(u) du.

Step 3: Integrate
The integral of tan(u) is -ln|cos(u)|, so:
∫tan(u) du = -ln|cos(u)|.

Step 4: Substitute Back
Substitute u = ln(x) back into the result:
-ln|cos(ln(x))|.

Final Answer:
∫tan(ln(x)) / x dx = -ln|cos(ln(x))| + C.
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