Find the integral $\int\frac{1}{x^2+10x+30}dx$

Step-by-step Solution

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Final answer to the problem

$\frac{\arctan\left(\frac{x}{\sqrt{30+10x}}\right)}{\sqrt{30+10x}}+C_0$
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Step-by-step Solution

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  • Integrate by trigonometric substitution
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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1

Solve the integral by applying the formula $\displaystyle\int\frac{x'}{x^2+a^2}dx=\frac{1}{a}\arctan\left(\frac{x}{a}\right)$

$\frac{1}{\sqrt{30+10x}}\arctan\left(\frac{x}{\sqrt{30+10x}}\right)$

Learn how to solve integrals of rational functions problems step by step online.

$\frac{1}{\sqrt{30+10x}}\arctan\left(\frac{x}{\sqrt{30+10x}}\right)$

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int(1/(x^2+10x+30))dx. Solve the integral by applying the formula \displaystyle\int\frac{x'}{x^2+a^2}dx=\frac{1}{a}\arctan\left(\frac{x}{a}\right). Multiply the fraction by the term . As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.

Final answer to the problem

$\frac{\arctan\left(\frac{x}{\sqrt{30+10x}}\right)}{\sqrt{30+10x}}+C_0$

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Function Plot

Plotting: $\frac{\arctan\left(\frac{x}{\sqrt{30+10x}}\right)}{\sqrt{30+10x}}+C_0$

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1
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5
6
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: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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