sin-101x-sinx-99-dx-

Question Number 82617 by necxxx last updated on 23/Feb/20

\int \sin (101 x) {(s i n x)}^{99} d x

Answered by TANMAY PANACEA last updated on 23/Feb/20

\int s i n (n + 1) {x s i n}^{n - 1} x d x n = 100

\int (s i n n x c o s x + c o s n x s i n x) {s i n}^{n - 1} x d x

\int ({s i n n x c o s x s i n}^{n - 1} x + {c o s n x s i n}^{n} x) d x

\int (s i n n x \times \frac{d ({s i n}^{n} x)}{d x} \times \frac{1}{n} + {s i n}^{n} x \times \frac{d (s i n n x)}{d x} \times \frac{1}{n}) d x

\frac{1}{n} \int \frac{d}{d x} (s i n n x . {s i n}^{n} x) d x

\frac{1}{n} (s i n n x . {s i n}^{n} x) + c

\frac{1}{100} (s i n 100 {x s i n}^{100} x) + c

Commented by peter frank last updated on 23/Feb/20

h e l p q n 74411

Commented by TANMAY PANACEA last updated on 23/Feb/20

o k l e t m e s e e