What is the integral of cos(2x)cos(x) ?

The integral of cos(2x)cos(x) is cos(2x)sin(x)+4/3 sin^3(x)+C

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integral of cos(2x)cos(x)

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

cos (2 x) sin (x) + \frac{4}{3} sin^{3} (x) + C

Solution steps

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

Apply Integration By Parts

: cos (2 x) sin (x) - \int - 2 sin (2 x) sin (x) d x

= cos (2 x) sin (x) - \int - 2 sin (2 x) sin (x) d x

\int - 2 sin (2 x) sin (x) d x = - \frac{4}{3} sin^{3} (x)

= cos (2 x) sin (x) - (- \frac{4}{3} sin^{3} (x))

Simplify

= cos (2 x) sin (x) + \frac{4}{3} sin^{3} (x)

Add a constant to the solution

= cos (2 x) sin (x) + \frac{4}{3} sin^{3} (x) + C

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

\frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6}

h \to 0 lim (\frac{( f ( h ) ( 0 + h ) - f ( 0 ) )}{h})

\int x f (x) d x

What is the integral of cos(2x)cos(x) ?
The integral of cos(2x)cos(x) is cos(2x)sin(x)+4/3 sin^3(x)+C