Integrals

Indefinite Integrals

100

 3x² dx

x³ + c

200

 cosx dx

sinx + C

300

1/x dx

ln|x| + C

400

2xe^{x^2} dx

e^{x^2} + C

500

1/(1+x²) dx

tan^-1(x) + C

Definite Integrals

100

x dx from 0 to 2

2

200

sinx dx from 0 to pi

2

300

1/x dx from 1 to e

1

400

2xe^{x^2} dx from 0 to 1

e-1

500

1/(1/+x^2) dx from 0 to 1 

pi/4

MAGIC

100

Derivative of the integral: t² dx from 0 to x 

x²

200

Derivative of the integral: cos(t) dt from 1 to x 

cos(x)

300

2x from 1 to 3 

8

400

Derivative of the integral: sin(t) dt from 0 to x²

2x * sin(x²)

500

Derivative of integral: t³ dt from x to x²

2x⁷-x³

Substitution

100

(x+1)² dx

(x+1)³/3 + C

200

x(x²+1)² dx

(x²+1)³/6 + C

300

2x(x²+1)³ dx from 0 to 1 

hint: change limits

15/4

400

x/(x²+4) dx

1/2 * ln(x²+4) + C

500

(sin(x) * cos(x)) dx from 0 to pi/2

1/2