Integrals!

Normal

100

Integral of (6x² - 3)dx

What is 2x³ + 3x + C

200

Integrate 5x

What is (5/2)x²

300

Integral of (x³ -x +2)/ (x^1/2)

What is (2/7)x^7/2 - (2/3)x^3/2 + x^1/2+C

400

Integral of (x³ + x)/(x-1)

What is (1/3)x³ + (1/2)x² +2x +2ln lx-1l + C

500

Integrate (3x +11)/ (x² -x -6)

What is 4ln lx-3l -ln lx+2l

U Substitution

100

Integral of (3-x)¹⁰

What is (-1/11) (3-x)¹¹+C

200

Integral of e^x * e^x dx

What is (1/2) e^2x+C

300

Integrate (2x +5)(x² +5x)⁷

What is (1/8)(x² +5x)⁸+C

400

Integral of (3x² - 10x + 4) *7 ^{(x3 - 5x2 +4x)}

What is 7^{(x3 - 5x2 + 4x)}/ ln7+C

500

Integral of x*3^{(x2 +1)}

What is 3^{(x2 + 1)}/(ln 9) + C

Trigonometry

100

Integral of sin(2x) dx

What is -(1/2) cos(2x) + C

200

Integral of cos(6x + 5)dx

What is 1/6 sin(6x + 5) + C

300

Integral of sinx + secx + cotx

What is -cosx + ln lsecx + tanxl + ln lsinxl +c

400

integral of csc²/cot³

What is 1/(2cotx²) or (1/2)tan²x+C

500

Integral of sin(lnx)/x

What is -cos(lnx) + C

Special Case

100

Integral of (7x)/(8x² + 9) dx

What is (7/16)ln l8x² +9l + C

200

Integral of e^(5x+2)

What is (1/5)e^(5x+2) + C

300

Integral of (7x +9)^1/2

What is (2/21) * (7x +9)^(3/2)+C

400

Integrate (x^2 + 5)/(x+2) dx

int(x - 2 + 9/(x+2) dx = .5x^2 - 2x + 9ln|x+2| + C

500

Integral of e^x / (e^2x + 4) 

What is 1/2 arctan(e^x / 2) + C

Definite

100

Integral of 3x dx from [0,1]

What is 3/2

200

Integral of cos x dx from [0, pi]

What is 0

300

Integral of cos(2x - 8)dx from [2,3]

What is 1/2(sin 4 - sin 2)

400

Integral of (4x³ - 6)(12x²)dx from [1,3]

What is 5200

500

Integral of (x² + 1)⁶ *(2x) dx from (-2, 1)

What is 77997/7