Basic Integration Formulas

Power Rule

100

∫ 7x³ dx

What is (7x⁴)/4 + C?

200

∫(4x⁵-2x²+6) dx

What is (2x⁶-2x³)/3 + 6x + C?

300

∫5/(x²) dx

What is -5/x + C?

400

∫(3x^1/2+8x^-3)dx

What is 2x^3/2-4/(x)² + C?

500

∫x(x)^1/2 dx

What is x⁴/8 + C?

U-Substitutions

100

∫(2x)(x²+4)⁵ dx

What is (x²+4)⁶/6 + C?

200

∫6x(3x²+1)² dx  

What is (3x²+1)³/3 + C?

300

∫(3x²)/(x³+7) dx

What is ln|x³+7| + C?

400

∫x(1+x²)^1/2 dx

What is (1+x²)^3/2/3 + C?

500

∫(2x)/(x²+1)³ dx

What is -1/(2(x²+1)²) + C?

Trig Integrals

100

∫cos(x) dx

What is sin(x) + C?

200

∫sec²(67x) dx

What is 1/67 * tan(67x) + C?

300

∫sec(x)tan(x) dx

What is sec(x) + C?

400

∫csc(10x)cot(10x) dx

What is -1/10 * csc(10x) + C?

500

∫(3sin(21x)−4sec²(7x)) dx

What is -1/7 * cos(21x) - 4/7 * tan(7x) + C?

Long Division

100

∫(x²+3x)/x dx

What is x²/2 + 3x + C?

200

∫(x²+1)/x dx

x²/2 + ln|x| + C?

300

∫(2x³+x)/x² dx

What is x² + ln|x| + C?

400

∫(x³+2x²+1)/x² dx

What is x²/2 + 2x - 1/x + C?

500

∫(x⁴+x²)/x² dx

What is x³/3 + x + C?

Random

100

∫1/25x dx

What is 1/25 * ln|x| + C?

200

∫(5x)(x²+3)⁴ dx

What is (x²+3)⁵/2 + C?

300

∫1/(1+x²) dx

What is arctan(x) + C?

400

∫(x²+4x)/x dx

What is x²/2 + 4x + C?

500

∫(2x)/(1-x²)^1/2 dx

What is -2(1-x²)^1/2 + C?