Question: Evaluate the integral. /

> Evaluate the integral. x - 4x + 1 · dx 1 x² – 3x + 2

> Evaluate the integral. 1 (x + a)(x + b)

> Use a power series to approximate the definite integral to six decimal places. c0.2 x In(1 + x²) dx

> Evaluate the integral. x - 4 dx -o?? - 5x + 6

> Evaluate the integral. 2 dx Jo 2x + 3x + 1

> Evaluate the integral. y dy (y + 4)(2y – 1)

> Evaluate the integral. 5х + 1 - dx (2х + 1)(х — 1)

> Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients. 16 + 1 (a) 16 + t³ x* + 1 (b) (x² – x)(x* + 2x² + 1)

> Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients. (a) x? – 4 (b) (x² – x + 1)(x² + 2)²

> Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients. x² – 1 x* – 2x + x? + 2x – 1 (a) (b) x³ + x + x x² – 2x + 1

> Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients. x' +1 (b) x³ – 3x² + 2x 1 (a) x? + x*

> Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients. х — 6 (a) x² + x – 6 x? (b) x? + x + 6

> Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients. 4 + x 1- x (a) (1 + 2х)(3 — х) (b) x' + x*

> Use a power series to approximate the definite integral to six decimal places. 1/2 " arctan(x/2) dx

> The functions y = ex2 and y = x2 ex2 don’t have elementary antiderivatives, but / does. Evaluate /

> Evaluate the integral. sin x cos x sin'x + cos“x

> Evaluate the integral. – sin x dx

> Evaluate the integral. sec x cos 2x sin x + sec x

> Evaluate the integral. Sx sin'x cos x dx

> Evaluate the integral. 1+ sin x dx SI 1- sin x

> Evaluate the integral. xe* dx /1 + e*

> Evaluate the integral. dx Vx² + 1

> Evaluate the integral. dx х In x — х

> Use a power series to approximate the definite integral to six decimal places. r0.3 Jo 1+ x3 dx

> Evaluate the integral. :+ arcsin. dx VI - x² 1 –

> Evaluate the integral. In(x + 1) ax x?

> Evaluate the integral. e 2x dx 1x 1+ e*

> Evaluate the integral. 1 dx 1+ 2e* — е *

> Evaluate the integral. 1 + x² dx 2

> Evaluate the integral. x? dx хв + 3x3 + 2

> Evaluate the integral. 1 dx /x + 1 + Vx

> Evaluate the integral. m/3_In(tan x) – dx Ja/4 sin x cos x

> Evaluate the integral. sin 2x dx J1+ cos“x

> Evaluate the integral. -dx I + x^^ Vx + 1

> Evaluate the indefinite integral as a power series. What is the radius of convergence? tan x dx

> Evaluate the integral. dx

> Evaluate the integral. de 1 + cos?e

> Evaluate the integral. de 1 + cos 0

> Evaluate the integral. dx J x*/4x? – 1

> Evaluate the integral. dx x* - 16

> Evaluate the integral. x In x dx /x² 1

> Evaluate the integral. fxk + c dx

> Evaluate the integral. dx x^x + x^

> Evaluate the integral. dx x + x/r

> Evaluate the integral. | (x + sin x)² dx

> Evaluate the indefinite integral as a power series. What is the radius of convergence? |x? In(1 + x) dx

> Evaluate the integral. |x' sinh mx dx х* si

> Evaluate the integral. dx Jx(x* + 1)

> Evaluate the integral. 1 x/4x2 + 1

> Evaluate the integral. 1 dx J x/4x + 1

> Evaluate the integral. x/2 - VI - x² dx

> Evaluate the integral. Sx(x – 1) *dx

> Evaluate the integral. (x – 1)e* dx .2 x

> Evaluate the integral. fx'e "dx

> Evaluate the integral. SVi+e" dx

> Evaluate the indefinite integral as a power series. What is the radius of convergence? i - 1+ t

> Evaluate the integral. dx 1 + x³

> Evaluate the integral. tan'x dx

> Evaluate the integral. |O tan'o do

> Evaluate the integral. | sin 6x cos 3x dx

> Evaluate the integral. sec 0 tan 0 o - J sec'o – sec 0

> Evaluate the integral. /3 sin 0 cot 0 do Jw/6 sec 0

> Evaluate the integral. 1 + sin x dx 1 + cos x

> Evaluate the integral. 12 1 + 4 cot x dx Ja/4 4 - cot x

> Evaluate the integral. |V3 – 2x – x² dx

> Evaluate the integral. 3/3 3 dx 2

> Evaluate the indefinite integral as a power series. What is the radius of convergence? dt

> Evaluate the integral. 1 + x dx

> Evaluate the integral. S,le - 1|dx

> Evaluate the integral. S In(x + vx? – T) dx

> Evaluate the integral. S sin Jat dt

> Evaluate the integral. dx J 1+ e*

> Evaluate the integral. 3x² + 1 dx Jo x³ + x? + x +1

> Evaluate the integral. + tan x)? sec x dx

> Evaluate the integral. + dx

> Evaluate the integral. In x -dx x/1 + (In x)²

> Evaluate the integral. | arctan /x dx

> Find a power series representation for f, and graph f and several partial sums sn(x) on the same screen. What happens as n increases? f(x) = tan (2x)

> (a) Approximate f by a Taylor polynomial with degree n at the number a. (b) Use Taylor’s Inequality to estimate the accuracy of the approximation / when x lies in the given interval. (c) Check your result in part (b) by graphing / S

> Evaluate the integral. t cos?t dt Jo CoS

> Evaluate the integral. x? dx VI - x2

> Evaluate the integral. X sec x tan x dx

> Evaluate the integral. In(1 + x²) dx

> Evaluate the integral. ( sin't cos't dt

> Evaluate the integral. 2х — 3 dx x' + 3x

> Evaluate the integral. 1 dx x'/x² – 1

> Evaluate the integral. cos(1/x) · dx ах

> Evaluate the integral. х+ 2 dx 2 х3 + 3х — 4

> Evaluate the integral. Se sin t cos t dt |t sin t

> Find a power series representation for f, and graph f and several partial sums sn(x) on the same screen. What happens as n increases? 1 + x S(x) = In 1- x

> Evaluate the integral. - dx (2х + 1)°

> Evaluate the integral. dt t* + 2

> Evaluate the integral. sin'x dx cos x

> Evaluate the integral. ( Vỹ In y dy

> Evaluate the integral. (3r + 1)7 dx

> Evaluate the integral. cos x dx 1- sin x

> Computer algebra systems sometimes need a helping hand from human beings. Try to evaluate with a computer algebra system. If it doesn’t return an answer, make a substitution that changes the integral into one that the CAS can evaluate.

> Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. dx V1 + x

> Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. | tan'x dx

> Find a power series representation for f, and graph f and several partial sums sn(x) on the same screen. What happens as n increases? f(x) = In(1 + x*)