## lands91 2 years ago ((sin^(5)x)/5)-((Sin^(7)x)/7)+c need to make it come out to this solution. (1/70)sin5(x)(5cos(2x)+9)+c

1. lands91

original integral $\cos ^{3}xsin ^{4}x$ got the solution with some help of $\frac{ \sin ^{5}x }{ 5 }-\frac{ \sin ^{7}x }{ 7 } +c$

2. hartnn

ok, what you get after factoring out sin^5 x ?

3. lands91

(1-cos2x)/2

4. lands91

thats about where I get lost

5. hartnn

that is just sin^2 x $$\large \frac{ \sin ^{5}x }{ 5 }-\frac{ \sin ^{7}x }{ 7 } = \sin^5 x[\frac{ 1 }{ 5 }-\frac{ \sin ^{2}x }{ 7 }] \\ \huge =\sin^5 x[\frac{ 1 }{ 5 }-\frac{ \dfrac{1-\cos 2x}{2} }{ 7 }] \\ \huge \\ \huge =\sin^5 x[\frac{ 1 }{ 5 }-\dfrac{1-\cos 2x}{14} ]$$

6. hartnn

can you proceed ?

7. lands91

do u just multiple the sin5x back into it now

8. lands91

or do i set a common denominator of 70

9. hartnn

set a common denominator of 70

10. lands91

which makes more sense

11. lands91

awesome. I see it now. was just over analysis of it. thank you

12. hartnn

i hope you'll get exactly what you want, welcome ^_^
The text passage is a conversation between a student and a tutor discussing a trigonometric integral problem and its solution. The student is trying to transform one form of the solution into another.
no_question

the passage does not contain a direct mathematical question that requires an answer. instead, it is a dialogue where the student is guided through the steps to understand the transformation of the solution.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## lands91 2 years ago ((sin^(5)x)/5)-((Sin^(7)x)/7)+c need to make it come out to this solution. (1/70)sin5(x)(5cos(2x)+9)+c

1. lands91

original integral $\cos ^{3}xsin ^{4}x$ got the solution with some help of $\frac{ \sin ^{5}x }{ 5 }-\frac{ \sin ^{7}x }{ 7 } +c$

2. hartnn

ok, what you get after factoring out sin^5 x ?

3. lands91

(1-cos2x)/2

4. lands91

thats about where I get lost

5. hartnn

that is just sin^2 x $$\large \frac{ \sin ^{5}x }{ 5 }-\frac{ \sin ^{7}x }{ 7 } = \sin^5 x[\frac{ 1 }{ 5 }-\frac{ \sin ^{2}x }{ 7 }] \\ \huge =\sin^5 x[\frac{ 1 }{ 5 }-\frac{ \dfrac{1-\cos 2x}{2} }{ 7 }] \\ \huge \\ \huge =\sin^5 x[\frac{ 1 }{ 5 }-\dfrac{1-\cos 2x}{14} ]$$

6. hartnn

can you proceed ?

7. lands91

do u just multiple the sin5x back into it now

8. lands91

or do i set a common denominator of 70

9. hartnn

set a common denominator of 70

10. lands91

which makes more sense

11. lands91

awesome. I see it now. was just over analysis of it. thank you

12. hartnn

i hope you'll get exactly what you want, welcome ^_^
user
The text passage is a conversation between a student and a tutor discussing a trigonometric integral problem and its solution. The student is trying to transform one form of the solution into another.

TYPE: NO_QUESTION

The passage does not contain a direct mathematical question that requires an answer. Instead, it is a dialogue where the student is guided through the steps to understand the transformation of the solution.