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#### Dhamnekar Winod

##### Active member

- Nov 17, 2018

- 103

How to find formulas for these$\displaystyle\int x^n\sin(x)\, dx, \displaystyle\int x^n\cos(x)\, dx,$ indefinite integrals when $n=1,2,3,4$ using differentiation under the integral sign starting with the formulas

$$\displaystyle\int \cos(tx)\,dx = \frac{\sin(tx)}{t}, \displaystyle\int \sin(tx)\,dx= -\frac{\cos(tx)}{t}$$ for $t > 0.$

I don't have any idea to solve these indefinite integrals except to solve them recursively using integration by parts.