What is the integral of cos(ax+b)cos(ax-b) ?

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

Popular >

integral of cos(ax+b)cos(ax-b)

\int cos (a x + b) cos (a x - b) d x

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

Solution steps

\int cos (a x + b) cos (a x - b) d x

Rewrite using trig identities

= \int \frac{1}{2} (cos (2 a x) + cos (2 b)) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int cos (2 a x) + cos (2 b) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int cos (2 a x) d x + \int cos (2 b) d x)

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

\int cos (2 b) d x = cos (2 b) x

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

Add a constant to the solution

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

\int 5000 e^{- 0.04 t} d t

\int \frac{4 sin ( x )}{1 + cos ^{2} ( x )} d x

\int \frac{ln ( 1 + tan ( x ) )}{cos ^{2} ( x )} d x

\int \frac{x}{( 9 + 4 x ^{2} ) ^{\frac{3}{2}}} d x

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

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