Use substitution to evaluate integral of 1 + tan x /1 - tanx
QUESTION 18 Use the substitution z = tan(x/2) to evaluate the integral / 3-cos e de ОА. tan-1 ( ✓2 tan 2 --()) +C OB. tan tan +C V2 OC V2 tan 2 Etan () )+c 2 OD. 1 tan tan +C 2 OE. tan V2 tan +C 2
Use substitution to evaluate the definite integral given below. -- tan* (3*) sec* (33°) de (Enter an exact answer.) Provide your answer below: S. - x tan* (3x)secº ( 3x?) ck=
Verify the identity. 1- tanx 1-tan secx Factor the numerator (tanx-1)(1+tan %) (1 - tan²x) (1-tan?:) (1+tan :) (1 - tanºx) Simplify the fraction O 1+tanºx Use an identity to simplify the expression from the previous step 1-tan O sec? 0 1
Q3-Evaluate the integral: dx Q4-Evaluate the integral: tan x dx (x + 1)
Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of integration.) $$ \int \frac{x^{3}}{\sqrt{x^{2}+25}} d x, \quad x=5 \tan (\theta) $$
Evaluate each integral (a) (x² + x) dx (b) 6.** (secx + tanx)2 dx
(1 point) Evaluate the indefinite integral. cos(/z5) Integral NOTE: Enter arctan(x) for tan-1 z, sin(x) for sin .] to enter all necessary, ( and)!! (1 point) Evaluate the indefinite integral. cos(/z5) Integral NOTE: Enter arctan(x) for tan-1 z, sin(x) for sin .] to enter all necessary, ( and)!!
4. Use an appropriate substitution to evaluate the following integral: 3/4 cos(V1 – x (1 – x dx 0
Evaluate the following integral. x² dx √ 121 + x² What substitution will be the most helpful for evaluating this integral? O A. x= 11 sec 0 O B. x= 11 tano O C. x= 11 sino Find dx. dx = dᎾ Rewrite the given integral using this substitution and simplifying. so x dx - Sodo √121 + x² Evaluate the indefinite integral. x²dx s √121+x² (Use C as the arbitrary constant.)
Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember to use absolute values where appropriate.) x3 dx, u = x4 – 5 5 Evaluate the indefinite integral. (Use C for the constant of integration.) X dx 1 + x20