What is the integral of (cos(ln(t)))/(2t) ?

The integral of (cos(ln(t)))/(2t) is 1/2 sin(ln(t))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(ln(t)))/(2t)

\int \frac{cos ( ln ( t ) )}{2 t} d t

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

Solution steps

\int \frac{cos ( ln ( t ) )}{2 t} d t

Take the constant out:

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

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

Apply u-substitution

: \int cos (u) d u

= \frac{1}{2} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{2} sin (u)

Substitute back

u = ln (t)

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

Add a constant to the solution

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

\int \frac{5 x - 4}{x ( x ^{2} - 2 x + 2 )} d x

\int \frac{x ^{3}}{1 - x} d x

\int 5 e^{5} x d x

\int x e^{x^{2}} sin (x^{2} + 4) d x

\int (2 x - 3)^{8} d x

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