Using Integration by Parts In Exercises11-14, find the indefinite integral using integration by parts with the given choices of u and dv. ∫ ( 2 x + 1 ) sin 4 x d x ; u = 2 x + 1 , d v = sin 4 x d x
Using Integration by Parts In Exercises11-14, find the indefinite integral using integration by parts with the given choices of u and dv. ∫ ( 2 x + 1 ) sin 4 x d x ; u = 2 x + 1 , d v = sin 4 x d x
Solution Summary: The author explains how to calculate the indefinite integral by the use of integration by parts.
Using Integration by Parts In Exercises11-14, find the indefinite integral using integration by parts with the given choices of u and dv.
∫
(
2
x
+
1
)
sin
4
x
d
x
;
u
=
2
x
+
1
,
d
v
=
sin
4
x
d
x
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Using Trigonometric Substitution
Exercises 7-10, find the indefinite integral using
the substitution x = 5 sec e.
In
%3D
- 25
dx
1
7.
dx
² – 25
8.
sinx
+e
sinx +x
COSX -e
The integral
dr may be written as me
nsinx
+ px + qe"+ C, where m, n, p, q, r, and Care constants not
sinx
equal to zero. Evaluate m +n+p+q+r.
sinx
cosx - e
+e sinx +*
The
integral
dx may be written as me
nsinx
+px+ qe™ + C,
sinx
where m, n, p, q, r, and C are constants not equal to zero. Evaluate m+n+p+q +r.
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY