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

The integral of sin(ln(t)) is 1/2 tsin(ln(t))-1/2 tcos(ln(t))+C

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integral of sin(ln(t))

\int sin (ln (t)) d t

\frac{1}{2} t sin (ln (t)) - \frac{1}{2} t cos (ln (t)) + C

Solution steps

\int sin (ln (t)) d t

Apply Integration By Parts

: t sin (ln (t)) - \int cos (ln (t)) d t

= t sin (ln (t)) - \int cos (ln (t)) d t

\int cos (ln (t)) d t = \frac{1}{2} t sin (ln (t)) + \frac{1}{2} t cos (ln (t))

= t sin (ln (t)) - (\frac{1}{2} t sin (ln (t)) + \frac{1}{2} t cos (ln (t)))

Simplify

t sin (ln (t)) - (\frac{1}{2} t sin (ln (t)) + \frac{1}{2} t cos (ln (t))) : \frac{1}{2} t sin (ln (t)) - \frac{1}{2} t cos (ln (t))

= \frac{1}{2} t sin (ln (t)) - \frac{1}{2} t cos (ln (t))

Add a constant to the solution

= \frac{1}{2} t sin (ln (t)) - \frac{1}{2} t cos (ln (t)) + C

\int \frac{sin ( 1 + x )}{1 + x} d x

\frac{d}{d x} (sin (\frac{1 - e ^{2 x}}{1 + e ^{2 x}}))

\int 2 t + 3 d t

x y^{^{'}} + y + x = 0

(x - 3) x (x + 3), 3 - x, 0, 2

What is the integral of sin(ln(t)) ?
The integral of sin(ln(t)) is 1/2 tsin(ln(t))-1/2 tcos(ln(t))+C