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

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

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integral of xsin(x+1)

\int x sin (x + 1) d x

- x cos (x + 1) + sin (x + 1) + C

Solution steps

\int x sin (x + 1) d x

Apply Integration By Parts

: - x cos (x + 1) - \int - cos (x + 1) d x

= - x cos (x + 1) - \int - cos (x + 1) d x

\int - cos (x + 1) d x = - sin (x + 1)

= - x cos (x + 1) - (- sin (x + 1))

Simplify

= - x cos (x + 1) + sin (x + 1)

Add a constant to the solution

= - x cos (x + 1) + sin (x + 1) + C

\int 3 tan^{2} (x) d x

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

\frac{\partial}{\partial x} (x e^{x} + 2 e^{x} y)

e^{x} x^{7} + 14 e^{x} x^{6} + 42 e^{x} x^{5}

\int (x^{3} - 2)^{\frac{1}{7}} \cdot x^{2} d x

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