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

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

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integral of xsin(x)+1

\int x sin (x) + 1 d x

- x cos (x) + sin (x) + x + C

Solution steps

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

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

\int 1 d x = x

= - x cos (x) + sin (x) + x

Add a constant to the solution

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

\int \frac{ln ( t )}{t ^{6}} d t

\int_{2}^{4} (x - 2) d x

\int (\frac{3 + 5 x - 6 x ^{2} - 7 x ^{3}}{2 x ^{2}}) d x

f (x) = x^{2} - 5 x + 5, at x = 4

2 x^{3} + 3 x^{2} - 12 x + 4

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