What is the integral of (sin(5ln(t)))/t ?

The integral of (sin(5ln(t)))/t is -1/5 cos(5ln(t))+C

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

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

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

Solution steps

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

Apply u-substitution

: \int \frac{sin ( u )}{5} d u

= \int \frac{sin ( u )}{5} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{5} (- cos (u))

Substitute back

u = 5 ln (t)

= \frac{1}{5} (- cos (5 ln (t)))

Simplify

= - \frac{1}{5} cos (5 ln (t))

Add a constant to the solution

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

x \to 7 - lim (- \frac{2}{7 - x})

n = 3 \sum \infty \frac{n ^{2}}{e ^{n}}

0.03 x^{2} - 4 x + 3 x^{0.8} - 5000

\int - \frac{t}{1 + t ^{2}} d t

f (x) = 14 cos (x), at x = 7

What is the integral of (sin(5ln(t)))/t ?
The integral of (sin(5ln(t)))/t is -1/5 cos(5ln(t))+C