Can you please solve these questions involving integrals? Thanks.
#int 9 cos (5x-3)dx#
#int 4 sin (x/3)dx#
#int (sec^2 7x - csc^2 7x)dx#
#int (sec3xtan3x - 15cos3x)dx#
#int (4csc10xcot10x+2sec^2 10x)dx#
I'm asking for your help in answering these questions for my advanced Math class. I'm okay with integrals in general, but I tend to get confused when it comes to trigonometric functions. Thank you!
#int 9 cos (5x-3)dx# #int 4 sin (x/3)dx# #int (sec^2 7x - csc^2 7x)dx# #int (sec3xtan3x - 15cos3x)dx# #int (4csc10xcot10x+2sec^2 10x)dx#
I'm asking for your help in answering these questions for my advanced Math class. I'm okay with integrals in general, but I tend to get confused when it comes to trigonometric functions. Thank you!
2 Answers
or alternatively:
#9/5sin(5x-3)+C# 2.#-12cos(x/3)# +C 3.#1/7tan(7x)+1/7cot(7x)+C# 4.#1/3sec(3x) - 5sin(3x) + C# 5.#-2/5csc(10x)- 1/5tan(10x)+C#
Explanation:
- u=5x-3
du=5dx
(1/5)du=dx
Rewrite:
2. u=x/3
du=dx/3
3du=dx
Rewrite:
3. Split up the integral:
Make the following substitution for both integrals:
u=7x
du=7dx
(1/7)du=dx
Now this is only composed of basic integrals:
4. Split up the integral:
Make the following substitution for both integrals:
u=3x
du=3dx
(1/3)du=dx
Now we have an integral composed of only basic integrals:
5. Split up the integral:
Make the following substitution for both integrals:
u=10x
du=10dx
(1/10)du=dx
Now this is only composed of basic integrals: