Solve ∫ xsinx wrt x=x^2/2sinx+C

$$\int x \sin x d x = \frac { x ^ { 2 } } { 2 } \sin x + C$$

Solve for C

$$C=-\frac{x^{2}\sin(x)}{2}-x\cos(x)+\sin(x)+С$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\int x\sin(x)\mathrm{d}x=x^{2}\sin(x)+2C$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}\sin(x)+2C=2\int x\sin(x)\mathrm{d}x$$

Subtract x^{2}\sin(x) from both sides.

$$2C=2\int x\sin(x)\mathrm{d}x-x^{2}\sin(x)$$

The equation is in standard form.

$$2C=x^{2}\sin(x)-x^{2}\sin(x)+2С$$

Divide both sides by 2.

$$\frac{2C}{2}=\frac{С}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$C=\frac{С}{2}$$