What is the integral of 3x*cos(x) ?

The integral of 3x*cos(x) is 3(xsin(x)+cos(x))+C

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integral of 3x*cos(x)

\int 3 x \cdot cos (x) d x

3 (x sin (x) + cos (x)) + C

Solution steps

\int 3 x cos (x) d x

Take the constant out:

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

= 3 \cdot \int x cos (x) d x

Apply Integration By Parts

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

= 3 (x sin (x) - \int sin (x) d x)

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

= 3 (x sin (x) - (- cos (x)))

Simplify

= 3 (x sin (x) + cos (x))

Add a constant to the solution

= 3 (x sin (x) + cos (x)) + C

\int ln (\frac{x + 1}{x}) d x

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\int \frac{28}{( 3 x - 1 ) ^{21}} d x

What is the integral of 3x*cos(x) ?
The integral of 3x*cos(x) is 3(xsin(x)+cos(x))+C