What is the integral of cos(x)5x) ?

The integral of cos(x)5x) is 5d(xsin(x)+cos(x))+C

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integral of cos(x)5x)

\int cos (x) d (5 x) d x

5 d (x sin (x) + cos (x)) + C

Solution steps

\int cos (x) d \cdot 5 x d x

Take the constant out:

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

= d \cdot 5 \cdot \int cos (x) x d x

Apply Integration By Parts

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

= d \cdot 5 (x sin (x) - \int sin (x) d x)

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

= d \cdot 5 (x sin (x) - (- cos (x)))

Simplify

= 5 d (x sin (x) + cos (x))

Add a constant to the solution

= 5 d (x sin (x) + cos (x)) + C

{\frac{s}{s ^{2} + 2 s - 3}}

\int ln (s) ec x tan (x) d x

10 x^{3} - 30 x + 120

\frac{d}{d x} (2 x^{2} y^{2})

z + 3 (\frac{1}{z ^{2}})

What is the integral of cos(x)5x) ?
The integral of cos(x)5x) is 5d(xsin(x)+cos(x))+C