What is the integral of sin(ax)cos(a)x ?

The integral of sin(ax)cos(a)x is cos(a)(-1/a xcos(ax)+1/(a^2)sin(ax))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(ax)cos(a)x

\int sin (a x) cos (a) x d x

cos (a) (- \frac{1}{a} x cos (a x) + \frac{1}{a ^{2}} sin (a x)) + C

Solution steps

\int sin (a x) cos (a) x d x

Take the constant out:

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

= cos (a) \cdot \int sin (a x) x d x

Apply Integration By Parts

: - \frac{1}{a} x cos (a x) - \int - \frac{1}{a} cos (a x) d x

= cos (a) (- \frac{1}{a} x cos (a x) - \int - \frac{1}{a} cos (a x) d x)

\int - \frac{1}{a} cos (a x) d x = - \frac{1}{a ^{2}} sin (a x)

= cos (a) (- \frac{1}{a} x cos (a x) - (- \frac{1}{a ^{2}} sin (a x)))

Simplify

= cos (a) (- \frac{1}{a} x cos (a x) + \frac{1}{a ^{2}} sin (a x))

Add a constant to the solution

= cos (a) (- \frac{1}{a} x cos (a x) + \frac{1}{a ^{2}} sin (a x)) + C

\frac{d}{d x} (x^{2} arctan (5 x) + ln (1 + 4 x^{2}))

\frac{d}{d x} (9 sin (4 x))

\frac{36}{( 1 + 3 x ) ^{3}}

\int \frac{26}{( x ^{2} - 1 ) ^{2}} d x

\frac{0.07 s}{7 s ^{2} + 19980}

What is the integral of sin(ax)cos(a)x ?
The integral of sin(ax)cos(a)x is cos(a)(-1/a xcos(ax)+1/(a^2)sin(ax))+C