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

The integral of cos(x)cosh(x) is (sin(x)cosh(x))/2+(cos(x)sinh(x))/2+C

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integral of cos(x)cosh(x)

\int cos (x) cosh (x) d x

\frac{sin ( x ) cosh ( x )}{2} + \frac{cos ( x ) sinh ( x )}{2} + C

Solution steps

\int cos (x) cosh (x) d x

Apply Integration By Parts

: cosh (x) sin (x) - \int sinh (x) sin (x) d x

= cosh (x) sin (x) - \int sinh (x) sin (x) d x

Apply Integration By Parts

: - sinh (x) cos (x) - \int - cosh (x) cos (x) d x

= cosh (x) sin (x) - (- sinh (x) cos (x) - \int - cosh (x) cos (x) d x)

Take the constant out:

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

= cosh (x) sin (x) - (- sinh (x) cos (x) - (- \int cosh (x) cos (x) d x))

Therefore

\int cosh (x) cos (x) d x = cosh (x) sin (x) - (- sinh (x) cos (x) - (- \int cosh (x) cos (x) d x))

Isolate

\int cosh (x) cos (x) d x

= \frac{sin ( x ) cosh ( x )}{2} + \frac{cos ( x ) sinh ( x )}{2}

Add a constant to the solution

= \frac{sin ( x ) cosh ( x )}{2} + \frac{cos ( x ) sinh ( x )}{2} + C

\int e^{4 t} cos (t) d t

\int \frac{1}{x 37 + x ^{2}} d x

\int - sinh (18 x) d x

\int 0.02 + 0.12 x d x

\int x 2 - x d x

What is the integral of cos(x)cosh(x) ?
The integral of cos(x)cosh(x) is (sin(x)cosh(x))/2+(cos(x)sinh(x))/2+C