Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
For the function T(x)= 7x^ 2 +11x-6 (x+1)(x^ 2 +2x+5)
MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals
Problem
For the function
T
(
x
)
=
7
x
2
+
11
x
−
6
(
x
+
1
)
(
x
2
+
2
x
+
5
)
,
T(x)=\frac{7x^{2}+11x-6}{(x+1)(x^{2}+2x+5)},
T
(
x
)
=
(
x
+
1
)
(
x
2
+
2
x
+
5
)
7
x
2
+
11
x
−
6
,
answer the following: (i) Decompose
T
(
x
)
T(x)
T
(
x
)
into partial fractions of the form
A
x
+
1
+
B
x
+
C
x
2
+
2
x
+
5
,
\frac{A}{x+1}+\frac{Bx+C}{x^{2}+2x+5},
x
+
1
A
+
x
2
+
2
x
+
5
B
x
+
C
,
and find
A
,
B
,
C
A,\,B,\,C
A
,
B
,
C
. (ii) Using the decomposition obtained in (i), evaluate
∫
T
(
x
)
d
x
\displaystyle\int T(x)\,dx
∫
T
(
x
)
d
x
.
Related theory
Antiderivatives
Integration Techniques
Integration by partial fractions
Integrals
Browse the problem library