What is the integral of xsin(1/7 x) ?

The integral of xsin(1/7 x) is -7xcos(1/7 x)+49sin(1/7 x)+C

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integral of xsin(1/7 x)

\int x sin (\frac{1}{7} x) d x

- 7 x cos (\frac{1}{7} x) + 49 sin (\frac{1}{7} x) + C

Solution steps

\int x sin (\frac{1}{7} x) d x

Apply Integration By Parts

: - 7 x cos (\frac{1}{7} x) - \int - 7 cos (\frac{1}{7} x) d x

= - 7 x cos (\frac{1}{7} x) - \int - 7 cos (\frac{1}{7} x) d x

\int - 7 cos (\frac{1}{7} x) d x = - 49 sin (\frac{1}{7} x)

= - 7 x cos (\frac{1}{7} x) - (- 49 sin (\frac{1}{7} x))

Simplify

= - 7 x cos (\frac{1}{7} x) + 49 sin (\frac{1}{7} x)

Add a constant to the solution

= - 7 x cos (\frac{1}{7} x) + 49 sin (\frac{1}{7} x) + C

\int 40 x^{\frac{3}{2}} - 60 x^{2} d x

\frac{4}{t ^{2}}

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

\frac{d}{d x} (\frac{4}{3} π r (x) (x)^{3})

\frac{d}{d x} (\frac{- x ^{2} - 8}{( x ^{2} - 8 ) ^{2}})

What is the integral of xsin(1/7 x) ?
The integral of xsin(1/7 x) is -7xcos(1/7 x)+49sin(1/7 x)+C