Page 11 - Formula-All

B. Tech. Semester-I (All Branch) Important Formulas

(C) Integrals leading to Inverse Trigonometric Functions:

Z
x
1
(1) √ dx = sin −1 + c
2
a − x 2 a

1
Z
(2) √ dx = sin −1 x + c
1 − x 2

1 1
Z
x
(3) dx = tan −1 + c
2
x + a 2 a a

Z
1
(4) dx = tan −1 x + c
1 + x 2

Z
1 1 x + a
(5) dx = log + c
2
a − x 2 2a x − a

1 1 x − a
Z
(6) dx = log + c
2
x − a 2 2a x + a

1 p
Z
2
2
(7) √ dx = log x + x + a + c

2
x + a 2
Z
1 p
2
2
(8) √ dx = log x + x − a + c

2
x − a 2
Z 2
p x p a p
2
2
2
2
2
2
(9) x + a dx = x + a + log x + x + a + c

2 2
Z 2
p x p a p
2
2
2
2
2
2
(10) x − a dx = x − a − log x + x − a + c

2 2
Z 2
x
p x p a
2
2
2
2
(11) a − x dx = a − x + sin −1 + c
2 2 a
Mr. Snehal D. Patel (Assistant Professor - Mathematics) Page 8 of 9