MathDB
Problems
Contests
National and Regional Contests
Japan Contests
Today's Calculation Of Integral
2005 Today's Calculation Of Integral
12
12
Part of
2005 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 12
Source: created by kunny
5/12/2005
Calculate the following indefinite integrals. [1]
∫
d
x
1
+
cos
x
\int \frac{dx}{1+\cos x}
∫
1
+
c
o
s
x
d
x
[2]
∫
x
x
2
−
1
d
x
\int x\sqrt{x^2-1}dx
∫
x
x
2
−
1
d
x
[3]
∫
a
−
x
2
d
x
(
a
>
0
,
a
≠
1
)
\int a^{-\frac{x}{2}}dx\ \ (a>0,a\neq 1)
∫
a
−
2
x
d
x
(
a
>
0
,
a
=
1
)
[4]
∫
sin
3
x
1
+
cos
x
d
x
\int \frac{\sin ^ 3 x}{1+\cos x}dx
∫
1
+
c
o
s
x
s
i
n
3
x
d
x
[5]
∫
e
4
x
sin
2
x
d
x
\int e^{4x}\sin 2x dx
∫
e
4
x
sin
2
x
d
x
calculus
integration
trigonometry
calculus computations