What is the integral of (1+x)cos(1+x) ?

The integral of (1+x)cos(1+x) is sin(1+x)+xsin(1+x)+cos(1+x)+C

integral of (1+x)cos(1+x)

integral

(1 + x) cos (1 + x)

sin (1 + x) + x sin (1 + x) + cos (1 + x) + C

Solution steps

\int (1 + x) cos (1 + x) d x

Expand

(1 + x) cos (1 + x) : cos (1 + x) + x cos (1 + x)

= \int cos (1 + x) + x cos (1 + x) 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

= \int cos (1 + x) d x + \int x cos (1 + x) d x

\int cos (1 + x) d x = sin (1 + x)

\int x cos (1 + x) d x = x sin (1 + x) + cos (1 + x)

= sin (1 + x) + x sin (1 + x) + cos (1 + x)

Add a constant to the solution

= sin (1 + x) + x sin (1 + x) + cos (1 + x) + C

in t e g r a l \frac{( - e ^{- 2 x} )}{2}

in t e g r a l \frac{lo g _{10} ( 1 )}{x}

in t e g r a l \frac{x}{( x ^{2} + 1 ) ^{3}}

in t e g r a l \frac{( x + 8 )}{( x + 7 )}

in t e g r a l 4 cos^{2} (x) - 2 sin^{2} (x)

What is the integral of (1+x)cos(1+x) ?
The integral of (1+x)cos(1+x) is sin(1+x)+xsin(1+x)+cos(1+x)+C