What is the integral of sin(101x)sin^99(x)dx?

1 Answer
Jan 11, 2018

int sin(101x)*(sinx)^99*dx=1/100sin(100x)*(sinx)^100+C

Explanation:

int sin(101x)*(sinx)^99*dx

=int sin(100x+x)*(sinx)^99*dx

=int (sin(100x)*cosx+cos(100x)*sinx)(sinx)^99*dx

=int sin(100x)*(sinx)^99*cosx*dx+int cos(100x)*(sinx)^100*dx

=1/100sin(100x)(sinx)^100-int cos(100x)*(sinx)^100*dx+int cos(100x)*(sinx)^100*dx

=1/100sin(100x)*(sinx)^100+C