Solve the trigonometric integral $\int\frac{\sec\left(x\right)^2\sin\left(x\right)}{2}dx$

Step-by-step Solution

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Final answer to the problem

$\frac{1}{2}\sec\left(x\right)+C_0$
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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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1

Simplify $\frac{\sec\left(x\right)^2\sin\left(x\right)}{2}$ into $\frac{\frac{\sin\left(x\right)}{\cos\left(x\right)^2}}{2}$ by applying trigonometric identities

$\int\frac{\frac{\sin\left(x\right)}{\cos\left(x\right)^2}}{2}dx$

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$\int\frac{\frac{\sin\left(x\right)}{\cos\left(x\right)^2}}{2}dx$

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Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int((sec(x)^2sin(x))/2)dx. Simplify \frac{\sec\left(x\right)^2\sin\left(x\right)}{2} into \frac{\frac{\sin\left(x\right)}{\cos\left(x\right)^2}}{2} by applying trigonometric identities. Divide fractions \frac{\frac{\sin\left(x\right)}{\cos\left(x\right)^2}}{2} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Take the constant \frac{1}{2} out of the integral. We can solve the integral \int\frac{\sin\left(x\right)}{\cos\left(x\right)^2}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \cos\left(x\right) it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.

Final answer to the problem

$\frac{1}{2}\sec\left(x\right)+C_0$

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Plotting: $\frac{1}{2}\sec\left(x\right)+C_0$

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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: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.

Used Formulas

See formulas (2)

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