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Find or evaluate the integral using substitution first, then using integration by parts. cos(In x) dx

Find or evaluate the integral using substitution first, then using integration by parts. cos(In x) dx

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I need help with step 4 of this problem I did 1 2 and 3

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Find or evaluate the integral using substitution first, then using integration by parts. Step 1 cos(In x) dx To find the integral Let w = In x. Differentiate w in terms of x. Thus, dw = dx = Jo X To cos(In x) dx, first use the substitution, then use the formula of integration by parts. Therefore, x = e. Differentiate x in terms of w. W du = -10 cos(In x) dx = 1 Step 2 Apply the rule of integration by parts. [vormor -] Judv u dv = uv - -SE ew dw = sin (w) x cos(w) ²² 201 ew dx Let dv= ew dw and integrate the differential equation to obtain the function v. V 1 = [dv = / ew And let u = cos w. Differentiate u in terms of w. dw cos (w) sin (w) dw du w dw.
Transcribed Image Text:Find or evaluate the integral using substitution first, then using integration by parts. Step 1 cos(In x) dx To find the integral Let w = In x. Differentiate w in terms of x. Thus, dw = dx = Jo X To cos(In x) dx, first use the substitution, then use the formula of integration by parts. Therefore, x = e. Differentiate x in terms of w. W du = -10 cos(In x) dx = 1 Step 2 Apply the rule of integration by parts. [vormor -] Judv u dv = uv - -SE ew dw = sin (w) x cos(w) ²² 201 ew dx Let dv= ew dw and integrate the differential equation to obtain the function v. V 1 = [dv = / ew And let u = cos w. Differentiate u in terms of w. dw cos (w) sin (w) dw du w dw.
Step 3 Rewrite the integration in terms of u and v. Step 4 J (cos w)ew dw = Again integrate Submit du = Jewe = J (cos w)ew (cos w)ew + ew (sin w) dw by parts. = -- Jewe dw Let dv= ew dw, and integrate the differential equation to obtain the function v. v - Jov - Sevan - [ = dv = ew dw And let u = sin w. Differentiate u with respect to w. (sin w)ew dw = (sin w)ew ·/ (sin(w) (sin w)ew Substitute the expressions for u and v on the right side, and obtain the integral. - Sew Skip (you cannot come back) ew(-sin(w) / - sin (w) dw dw sin (w) ew dw Dew dw
Transcribed Image Text:Step 3 Rewrite the integration in terms of u and v. Step 4 J (cos w)ew dw = Again integrate Submit du = Jewe = J (cos w)ew (cos w)ew + ew (sin w) dw by parts. = -- Jewe dw Let dv= ew dw, and integrate the differential equation to obtain the function v. v - Jov - Sevan - [ = dv = ew dw And let u = sin w. Differentiate u with respect to w. (sin w)ew dw = (sin w)ew ·/ (sin(w) (sin w)ew Substitute the expressions for u and v on the right side, and obtain the integral. - Sew Skip (you cannot come back) ew(-sin(w) / - sin (w) dw dw sin (w) ew dw Dew dw
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