Integration Jeopardy

Integration by Substitution

100

int (4x^3)/sqrt(x^4+9)dx

2 sqrt(x^4+9) + C

200

int tan(x) sec^4(x) dx

1/4 sec^4(x) + C

or

1/4 tan^4(x) + 1/2 tan^2(x)+C

300

int dx/(xsqrt(ln(x))

2 sqrt(ln(x)) +C

400

int x sqrt(x - 5)dx

2/5 (sqrt(x-5))^5 + 10/3 (sqrt(x-5))^3+C

500

int sqrt(16-x^2)dx

1/2 x sqrt(16-x^2) + 8 sin^(-1)(1/4 x) + C

Integration by Parts

100

int x ln(x) dx

1/2 x^2 ln(x) -1/4 x^2 + C

200

int (x + 2)e^(2x+1)dx

1/2 x(+2)e^(2x+1) - 1/4 e^(2x + 1) + C

300

int x^2 cos(x) dx

x^2 sin(x) - 2 sin(x) +2x cos(x) +C

400

int e^(sqrt(x))dx

2 e^(sqrt(x)) sqrt(x) - 2 e^(sqrt(x))+C

500

int e^x sin(nx)dx

- n/(1+n^2) e^x cos(nx)+ 1/(1+n^2) sin(nx) +C

Definite Integrals

100

int_1^2 (x+2x^2)/x dx

4

200

int_e^(e^2) dx/(x ln(x))

ln(2)

300

int_0^2 x e^x dx

e^2 +1

400

int_(sin(pi/2))^(ln(e)) cos(e^(x^2))dx

0

500

int_(-pi)^(pi) x e^(sin(x^2))dx

0

Fun with Trigonometry

100

int (sin(x))/(root3(cos(x)))dx

-3/2 root3(cos^2(x)) + C

200

int sin(x) cos(cos(x)) dx

-sin(cos(x)) + C

300

int tan^2(theta) sec^4(theta)d theta

1/5 tan^3(theta) sec^2(theta) + 2/15 tan^3(theta) + C

400

int (1 + cos(x))/(sin(x))dx

ln|csc(x) - cot(x)| + ln|sin(x)| + C

500

int theta tan^2(theta) d theta 

theta tan(theta) - 1/2 theta^2 - 1/2 ln|1 + tan^2(theta)| + C

Potpourri

100

int[int_3^x e^(2t)dt]dx

e^(2x)/4 - e^(6x)/2+C

200

int[d/dx f(x)]dx

f(x) + C

300

d/(dr) int_3^(r^2) sin(x^2) dx

2 r sin(r^4)

400

int cos(t) dx

x cos(t) + C

500

int ln(1 + x^2) dx

x ln(1 + x^2) - 2x + 2 tan^(-1)(x) +C