integral of (cos(ln(t)))/(5t)

解答

\int \frac{cos ( ln ( t ) )}{5 t} d t

\frac{1}{5} sin (ln (t)) + C

求解步骤

\int \frac{cos ( ln ( t ) )}{5 t} d t

提出常数:

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

= \frac{1}{5} \cdot \int \frac{cos ( ln ( t ) )}{t} d t

使用换元积分法

= \frac{1}{5} \cdot \int cos (u) d u

使用积分常见定则:

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

= \frac{1}{5} sin (u)

u = ln (t)

代回

= \frac{1}{5} sin (ln (t))

解答补常数

= \frac{1}{5} sin (ln (t)) + C

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