Integrals

Indefinite Integrals

100

∫ 2x dx

x²+C

200

∫ 3x+2 dx

(3x²/2)+2x+C

300

∫  17+3x⁴ dx

17x+(3x⁵/5)+C

400

∫ 6x²+12x+3 dx

3x³+6x²+3x+C

500

∫ 6x⁹+23x+4x³ dx

(3x¹⁰/5)+(23x²/2)+x⁴+C

Definite Integrals

100

_o∫² x³ dx

4

200

₁∫⁵ 2x⁴+3 dx

6308/5 or 1261.6

300

₀∫¹ 3x+7 dx

17/2 or 8.5

400

₆∫^9.5 3x³+3x dx

5218.172

500

₀∫¹² x²+34 dx

984

Solve Using Substitution

100

∫ 5sec²(5x+1) dx

tan(5x+1)+C

200

∫ e^x sin(e^x) dx

-cos(e^x)+C

300

₀∫¹ -12x²(4x³-1)³ dx

-20

400

∫ sin(ln(x))/x dx

-cos(ln(x))+C

500

∫ (e^x)/(e^x+1) dx

ln(e^x+1)+C

Integrals of Particular Functions

100

∫xⁿ dx

(xⁿ⁺¹/n)+C

200

∫sin(x)dx

-cos(x)+C

300

∫e^x dx

e^x+C

400

∫ sec(x)tan(x) dx

sec(x)+C

500

∫ csc²(x) dx

-cot(x)+C

Tougher Integrals

100

1/(x^2 - x + 1)

(3*sqrt(3))/8 * arctan(2/sqrt(3) * (x - 1/2)) + C

200

∫ sec³(x) dx

(ln(|tan(x) + sec(x)|) + sec(x)tan(x))/2 + C

300

-_π∫^π (1 + 2⌊(x/π)⌋)e^x2 (sec(x) - cos(x)) dx

0

400

∫ tan³(ln(x)) / x dx

1/2 tan²(ln|x|) - ln|cos(ln|x|)| + C

500

_-1∫ ¹ (1/x) * sqrt((1+x)/(1-x)) * ln((2x²+2x+1)/(2x²-2x+1)) dx

4π arccot(sqrt(phi))