Evaluate
∫ sin ( ln ( x 5 ) ) x d x \displaystyle \int\frac{{\sin{{\left({\ln{{\left({x}^{{5}}\right)}}}\right)}}}}{{x}}{\left.{d}{x}\right.} ∫ x sin ( ln ( x 5 ) ) d x for x > 0.
First make the substitution u =
Preview Question 6 Part 1 of 4
Then
∫ sin ( ln ( x 5 ) ) x d x \displaystyle \int\frac{{\sin{{\left({\ln{{\left({x}^{{5}}\right)}}}\right)}}}}{{x}}{\left.{d}{x}\right.} ∫ x sin ( ln ( x 5 ) ) d x =
∫ \displaystyle \int ∫ Preview Question 6 Part 2 of 4
du
Now integrate with respect to u to get
Preview Question 6 Part 3 of 4
+ C
So
∫ sin ( ln ( x 5 ) ) x d x \displaystyle \int\frac{{\sin{{\left({\ln{{\left({x}^{{5}}\right)}}}\right)}}}}{{x}}{\left.{d}{x}\right.} ∫ x sin ( ln ( x 5 ) ) d x =
Preview Question 6 Part 4 of 4
+ C
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Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c