What is the integral of 7xcos(x) ?

The integral of 7xcos(x) is 7(xsin(x)+cos(x))+C

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integral of 7xcos(x)

\int 7 x cos (x) d x

7 (x sin (x) + cos (x)) + C

Solution steps

\int 7 x cos (x) d x

Take the constant out:

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

= 7 \cdot \int x cos (x) d x

Apply Integration By Parts

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

= 7 (x sin (x) - \int sin (x) d x)

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

= 7 (x sin (x) - (- cos (x)))

Simplify

= 7 (x sin (x) + cos (x))

Add a constant to the solution

= 7 (x sin (x) + cos (x)) + C

\frac{d}{d t} (t - t^{2})

\frac{4}{( s - 2 ) ^{2}}

\frac{d}{d x} (\frac{e ^{2 x}}{x + 1})

\int 2 (x + 1) d x

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = - 1, y^{^{'}} (0) = - 3

What is the integral of 7xcos(x) ?
The integral of 7xcos(x) is 7(xsin(x)+cos(x))+C