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Rewrite the integral ∫_ ^ (27x^2-15x-6)/(10x^3-x^2-3x) dx in partial fraction…
Related Topics
Wize University Calculus 1 Textbook > Integration Techniques
Partial Fractions
6 Activities
Rewrite the integral
∫
27
x
2
−
15
x
−
6
10
x
3
−
x
2
−
3
x
d
x
\displaystyle \int_{ }^{ }\frac{27x^2-15x-6}{10x^3-x^2-3x} \ dx
∫
10
x
3
−
x
2
−
3
x
27
x
2
−
15
x
−
6
d
x
in partial fraction decomposition form. (Do not solve)
∫
[
4
x
+
3
2
x
+
1
+
2
5
x
−
3
]
d
x
\int_{ }^{ }\left[\frac{4}{x}+\frac{3}{2x+1}+\frac{2}{5x-3}\right]dx
∫
[
x
4
+
2
x
+
1
3
+
5
x
−
3
2
]
d
x
∫
[
4
x
+
3
2
x
+
1
−
2
5
x
−
3
]
d
x
\int_{ }^{ }\left[\frac{4}{x}+\frac{3}{2x+1}-\frac{2}{5x-3}\right]dx
∫
[
x
4
+
2
x
+
1
3
−
5
x
−
3
2
]
d
x
∫
[
3
x
+
2
2
x
+
1
−
4
5
x
−
3
]
d
x
\int_{ }^{ }\left[\frac{3}{x}+\frac{2}{2x+1}-\frac{4}{5x-3}\right]dx
∫
[
x
3
+
2
x
+
1
2
−
5
x
−
3
4
]
d
x
∫
[
2
x
+
3
2
x
+
1
−
4
5
x
−
3
]
d
x
\int_{ }^{ }\left[\frac{2}{x}+\frac{3}{2x+1}-\frac{4}{5x-3}\right]dx
∫
[
x
2
+
2
x
+
1
3
−
5
x
−
3
4
]
d
x
I don't know
Check Submission
More Partial Fractions Questions:
Practice Question: Partial Fraction
Compute
∫
3
x
2
−
1
x
4
+
x
3
d
x
{\displaystyle\int}\frac{3x^2-1}{x^4+x^3}\de{x}
∫
x
4
+
x
3
3
x
2
−
1
d
x
.
Practice: Partial Fractions with A and B
Q:
\textbf{Q:}
Q:
Find
∫
x
2
−
2
x
−
3
(
x
2
−
9
)
(
x
−
4
)
d
x
\displaystyle\int\frac{x^2-2x-3}{\left(x^2-9\right)\left(x-4\right)}dx
∫
(
x
2
−
9
)
(
x
−
4
)
x
2
−
2
x
−
3
d
x
Evaluate
∫
x
2
−
9
2
x
3
+
x
2
−
15
x
d
x
\displaystyle\int\frac{x^{2}-9}{2x^3+x^2-15x} \ dx
∫
2
x
3
+
x
2
−
15
x
x
2
−
9
d
x
and write the answer as a single logarithm.
If
9
x
−
3
x
3
+
2
x
2
−
5
x
−
6
=
A
x
+
1
+
B
x
−
2
−
C
x
+
3
\displaystyle\frac{9x-3}{x^3+2x^2-5x-6}=\frac{A}{x+1}+\frac{B}{x-2}-\frac{C}{x+3}
x
3
+
2
x
2
−
5
x
−
6
9
x
−
3
=
x
+
1
A
+
x
−
2
B
−
x
+
3
C
find the values of
A
A
A
,
B
B
B
and
C
C
C
.
Trig with Partial Fractions
Evaluate
∫
cos
θ
3
sin
2
θ
+
2
sin
θ
d
θ
\displaystyle\int\frac{\cos\theta}{3\sin^2\theta + 2\sin\theta}d\theta
∫
3
sin
2
θ
+
2
sin
θ
cos
θ
d
θ
Practice: Partial Fractions with A, B and C
Q:
\textbf{Q:}
Q:
Find
∫
2
x
3
−
3
x
+
2
x
3
−
x
2
−
2
x
d
x
\displaystyle\int\frac{2x^3-3x+2}{x^3-x^2-2x} \ dx
∫
x
3
−
x
2
−
2
x
2
x
3
−
3
x
+
2
d
x
Practice: Partial Fractions with A and B
Q:
\textbf{Q:}
Q:
Find
∫
x
2
−
2
x
−
3
(
x
2
−
9
)
(
x
−
4
)
d
x
\displaystyle\int\frac{x^2-2x-3}{\left(x^2-9\right)\left(x-4\right)}dx
∫
(
x
2
−
9
)
(
x
−
4
)
x
2
−
2
x
−
3
d
x
Evaluate the integral
∫
4
x
2
−
3
x
d
x
\displaystyle\int_{ }^{ }\frac{4}{x^2-3x}dx
∫
x
2
−
3
x
4
d
x
. Write your answer as a single logarithm.
(a)
ln
∣
(
x
x
−
3
)
4
3
∣
+
C
\ln\left|\left(\frac{x}{x-3}\right)^{\frac{4}{3}}\right|+C
ln
(
x
−
3
x
)
3
4
+
C
(b)
ln
∣
(
x
−
3
x
)
−
2
3
∣
+
C
\ln\left|\left(\frac{x-3}{x}\right)^{-\frac{2}{3}}\right|+C
ln
(
x
x
−
3
)
−
3
2
+
C
(c)
ln
∣
(
x
x
−
3
)
2
3
∣
+
C
\ln\left|\left(\frac{x}{x-3}\right)^{\frac{2}{3}}\right|+C
ln
(
x
−
3
x
)
3
2
+
C
(d)
ln
∣
(
x
−
3
x
)
4
3
∣
+
C
\ln\left|\left(\frac{x-3}{x}\right)^{\frac{4}{3}}\right|+C
ln
(
x
x
−
3
)
3
4
+
C
Practice Question: Partial Fraction
Practice Question
Compute
∫
3
x
2
−
1
x
4
+
x
3
d
x
{\displaystyle\int}\frac{3x^2-1}{x^4+x^3}\de{x}
∫
x
4
+
x
3
3
x
2
−
1
d
x
.
Evaluate
∫
x
(
x
+
1
)
2
(
x
2
+
4
)
d
x
\int_{ }^{ }\frac{x}{\left(x+1\right)^2\left(x^2+4\right)}dx
∫
(
x
+
1
)
2
(
x
2
+
4
)
x
d
x
Evaluate
∫
x
sec
2
x
d
x
\int_{ }^{ }x\sec^2xdx
∫
x
sec
2
x
d
x
Practice Question: Partial Fraction
Practice Question
Compute
∫
3
x
2
−
1
x
4
+
x
3
d
x
{\displaystyle\int}\frac{3x^2-1}{x^4+x^3}\de{x}
∫
x
4
+
x
3
3
x
2
−
1
d
x
.
Evaluate the integral
∫
4
x
2
−
3
x
d
x
\displaystyle\int_{ }^{ }\frac{4}{x^2-3x}dx
∫
x
2
−
3
x
4
d
x
.
Evaluate
∫
x
2
−
9
2
x
3
+
x
2
−
15
x
d
x
\displaystyle\int\frac{x^{2}-9}{2x^3+x^2-15x} \ dx
∫
2
x
3
+
x
2
−
15
x
x
2
−
9
d
x
and write the answer as a single logarithm.
If
9
x
−
3
x
3
+
2
x
2
−
5
x
−
6
=
A
x
+
1
+
B
x
−
2
−
C
x
+
3
\displaystyle\frac{9x-3}{x^3+2x^2-5x-6}=\frac{A}{x+1}+\frac{B}{x-2}-\frac{C}{x+3}
x
3
+
2
x
2
−
5
x
−
6
9
x
−
3
=
x
+
1
A
+
x
−
2
B
−
x
+
3
C
find the values of
A
A
A
,
B
B
B
and
C
C
C
.
Practice: Partial Fractions with A, B and C
Q:
\textbf{Q:}
Q:
Find
∫
2
x
3
−
3
x
+
2
x
3
−
x
2
−
2
x
d
x
\displaystyle\int\frac{2x^3-3x+2}{x^3-x^2-2x} \ dx
∫
x
3
−
x
2
−
2
x
2
x
3
−
3
x
+
2
d
x
Practice: Partial Fractions with A and B
Find
∫
x
2
−
2
x
−
3
(
x
2
−
9
)
(
x
−
4
)
d
x
\displaystyle\int\frac{x^2-2x-3}{\left(x^2-9\right)\left(x-4\right)}dx
∫
(
x
2
−
9
)
(
x
−
4
)
x
2
−
2
x
−
3
d
x
Trig with Partial Fractions
Evaluate
∫
cos
θ
3
sin
2
θ
+
2
sin
θ
d
θ
\displaystyle\int\frac{\cos\theta}{3\sin^2\theta + 2\sin\theta}d\theta
∫
3
sin
2
θ
+
2
sin
θ
cos
θ
d
θ