What is the integral of+sin(xt) ?

The integral of+sin(xt) is -1/x cos(xt)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of+sin(xt)

\int + sin (x t) d t

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

Solution steps

\int sin (x t) d t

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = x t

= \frac{1}{x} (- cos (x t))

Simplify

= - \frac{1}{x} cos (x t)

Add a constant to the solution

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

\int (x cos (y) + 5 x e^{5 x y}) d y

\int \frac{x - 3}{1 - x ^{2}} d x

\int 27 x sec^{2} (3 x) d x

\int - y ln (y) d y

\frac{1}{( e ^{x} + 1 )}