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JH
Numerade Educator

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Problem 44 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int \sin x \sec^5 x dx $

Answer

$\frac{\sec ^{4} x}{4}+c$

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Video Transcript

this problem is from Chapter seven section to problem number forty four in the book Calculus Early. Transcendental. Lt's a condition by James Door. We have an integral of sign. Next time, see cancer the fifth power here weaken. Use the fact that she can't is one over co sign. So let's pull out One factor of C can right is one over co sign and then we have our remaining seeking to the fourth power left over. So here we have integral of tangent time seeking to the fourth power of X. Next we can go ahead. And since we already have one factor of tangent here, let let's pull out another seeking from the Sikh into the fourth. So we have tangent times. He can't times he can. Cute. This is just we do a u substitution. Let's take you to B. C. Can't then do you is seeking time, Stan, which is precisely in our incident we have here. We have tangent times. He can't gx so using our new substitution, we can rewrite this as you cube coming from C Can cube. Do you? And then we could use the power rule to evaluate this. You to the fourth power over four. Plus he and finally, we should go back to our U substitution to replace you with Seek Innovex. So we obtain. She came to the fore Power Vex over four. Plus he and that's your answer.