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Evaluate the indefinite integral. dx 1 + x10

Evaluate the indefinite integral. dx 1 + x10

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 3CR: Determine whether each of the following statements is true or false, and explain why. The derivative...
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Evaluate the indefinite integral. dx 1 + x10 Step 1 x4 We must decide what to choose for u. If u = f(x), then du = f '(x) dx, and so it is helpful to look for some expression in dx for which the derivative is also present, though perhaps missing a 1 + x10 constant factor. Finding u in this integral is a little trickier than in some others. We see that 1 + x10 is part of this integral, but the derivative of 1 + x10 is 10x which is not present in the integrand. 109 4 However, notice that the x4 in the numerator is close to the derivative of x, which is 5x 5,4 Step 2 If we choose u = x5, thenx10 4. and du = 5x |dx. 574 = x4 x4 1 If u = x is substituted into dx, then we have dx = dx). 1 + x10 1 + x10 1 + u²
Transcribed Image Text:Evaluate the indefinite integral. dx 1 + x10 Step 1 x4 We must decide what to choose for u. If u = f(x), then du = f '(x) dx, and so it is helpful to look for some expression in dx for which the derivative is also present, though perhaps missing a 1 + x10 constant factor. Finding u in this integral is a little trickier than in some others. We see that 1 + x10 is part of this integral, but the derivative of 1 + x10 is 10x which is not present in the integrand. 109 4 However, notice that the x4 in the numerator is close to the derivative of x, which is 5x 5,4 Step 2 If we choose u = x5, thenx10 4. and du = 5x |dx. 574 = x4 x4 1 If u = x is substituted into dx, then we have dx = dx). 1 + x10 1 + x10 1 + u²
Step 3 We must also convert x4 dx into an expression involving u. 1 Using du = 5x4 dx, then we get xª dx = 1 du. Step 4 x4 1 1 1 Now, if u = x5, then dx = du du. 1 + u? 1 + x10 1 + u 12 5 1 1 This evaluates as + C. du = 1 + u2 Submit Skip (you cannot come back)
Transcribed Image Text:Step 3 We must also convert x4 dx into an expression involving u. 1 Using du = 5x4 dx, then we get xª dx = 1 du. Step 4 x4 1 1 1 Now, if u = x5, then dx = du du. 1 + u? 1 + x10 1 + u 12 5 1 1 This evaluates as + C. du = 1 + u2 Submit Skip (you cannot come back)
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