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Find the integral $\int\left(\sec\left(ti\right)^2+\frac{1}{1+t^2}j\right)dt$

Step-by-step Solution

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Final Answer

$\frac{-2t}{t^{2}-1}+2\ln\left(\frac{t+1}{\sqrt{t^{2}-1}}\right)+\ln\left(\frac{t-1}{t+1}\right)+j\arctan\left(t\right)+C_0$
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Step-by-step Solution

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Simplify the expression inside the integral

$\int\sec\left(ti\right)^2dt+\int\frac{j}{1+t^2}dt$

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$\int\sec\left(ti\right)^2dt+\int\frac{j}{1+t^2}dt$

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Learn how to solve problems step by step online. Find the integral int(sec(ti)^2+1/(1+t^2)j)dt. Simplify the expression inside the integral. The integral \int\sec\left(ti\right)^2dt results in: \ln\left(\frac{t-1}{t+1}\right)+\frac{-2t}{t^{2}-1}+2\ln\left(\frac{t}{\sqrt{t^{2}-1}}+\frac{1}{\sqrt{t^{2}-1}}\right). Gather the results of all integrals. The integral \int\frac{j}{1+t^2}dt results in: j\arctan\left(t\right).

Final Answer

$\frac{-2t}{t^{2}-1}+2\ln\left(\frac{t+1}{\sqrt{t^{2}-1}}\right)+\ln\left(\frac{t-1}{t+1}\right)+j\arctan\left(t\right)+C_0$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of (secti^2+1/(1+t^2)j)dt using basic integralsSolve integral of (secti^2+1/(1+t^2)j)dt using u-substitutionSolve integral of (secti^2+1/(1+t^2)j)dt using integration by partsSolve integral of (secti^2+1/(1+t^2)j)dt using tabular integration

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Function Plot

Plotting: $\frac{-2t}{t^{2}-1}+2\ln\left(\frac{t+1}{\sqrt{t^{2}-1}}\right)+\ln\left(\frac{t-1}{t+1}\right)+j\arctan\left(t\right)+C_0$

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7
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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

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