1.\int_{}^{} \sin\frac{2}{3}xdx 2.\int_{}^{}x \cos6x^2dx 3.\int_{}^{}\tan9xdx 4, \int_{}^{}x^2\cot x^3dx

Monincbh

Monincbh

Answered question

2021-12-03

1.{{sin23xdx
2.{{xcos6x2dx
3.{{tan9xdx
4,{{x2cotx3dx

Answer & Explanation

Steven Arredondo

Steven Arredondo

Beginner2021-12-04Added 18 answers

Solution of question 1
{{sin(23x)dx
Put u=2x3dudx=23 or 3du2=dx
{{sinu32du=32sinudu
Now solving integral
=32cos(u)+c
=3cosu2+c
=3cos(23x)2+c
Put back u=(23)x
Hence above is the required solution pf given integral
Solution of question 3
{{×cos(6x2)dx
Put u=6x2dudx=12xdx=112xdu
{{xcosu112xdu
112{{cosudu
Now solving integral
112sin(u)+c
Put back u=6x2
sin6x212+c
Hence above is the required solution of given integral
Solution of question 3
{{tan9x
Put u=9xdudx=0au=19du
10{{tan(u)dx
Now solving integral
Rewosite tan(u)=sinucosu
{{19

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