Integrate the function $\frac{x}{x^2+4}$ from $-1$ to $2$

Step-by-step Solution

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Final answer to the problem

$-\ln\left|\frac{2}{\sqrt{2^2+4}}\right|- -\ln\left|\frac{2}{\sqrt{{\left(-1\right)}^2+4}}\right|$
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Step-by-step Solution

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  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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We can solve the integral $\int\frac{x}{x^2+4}dx$ by applying integration method of trigonometric substitution using the substitution

Learn how to solve integration techniques problems step by step online.

$x=2\tan\left(\theta \right)$

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Learn how to solve integration techniques problems step by step online. Integrate the function x/(x^2+4) from -1 to 2. We can solve the integral \int\frac{x}{x^2+4}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. The integral of the tangent function is given by the following formula, \displaystyle\int\tan(x)dx=-\ln(\cos(x)).

Final answer to the problem

$-\ln\left|\frac{2}{\sqrt{2^2+4}}\right|- -\ln\left|\frac{2}{\sqrt{{\left(-1\right)}^2+4}}\right|$

Exact Numeric Answer

$0.235002$

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Function Plot

Plotting: $\frac{x}{x^2+4}$

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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Integration Techniques

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Used Formulas

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