Integration!

Natural Logs/ Logs

100

ʃ (1/x)dx

ln(x)+C

200

ʃ(2x/x²)dx

2ln(x)+c

300

ʃ(3x²/x⁴)dx

-3/x+c

400

ʃ((2x/x²) - (3x²/x³))dx

-ln(x) + c

500

Is the following statement True/False:

ʃ(3/x)dx = 3ln(3x)+c

True

Reverse chain rule

100

ʃ (8x(x²+9)³)dx

(x²+9)⁴ + c

200

ʃ (3x²+2x) × (x³+x²)⁵dx

1/6 (x³+x²)⁶ + c

300

ʃ e^sin(x)dx

cos(x)e^sin(x) + c

400

Could we use + c² instead of c as our constant of integration?

no

500

ʃ -sin(x) × cos(cos(x))dx

sin(cos(x)) + c

Polynomials/Exponential

100

ʃ dx

x+c

200

ʃ(x²+x)dx

1/3x³ + 1/2x² + c

300

ʃ(4x³-2x²-x-2)dx

x⁴-2/3x³-1/2x²-2x+c

400

ʃ(6x^5+x^0.5)dx

x^6+0.5x^-0.5+c

500

ʃ(24e^4x)dx

6e^4x + c

Trig

100

ʃ(cos(x))dx

sin(x)+c

200

ʃ(sin(x)-cos(x))dx

-cos(x)-sin(x)+c

300

ʃ(sin(x)+2x)dx

-cos(x)+x²+c

400

ʃ(-6cos(0.4x)+e)dx

-15sin(0.4x) + ex + c

500

ʃ(tan(x))dx

-log(cos(x))+C