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Find the integral $\int400\left(1+\frac{2t}{24+t^2}\right)dt$

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Solution

Final answer to the problem

$400t+400\ln\left(t^2+24\right)+C_0$
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Step-by-step Solution

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The integral of a function times a constant ($400$) is equal to the constant times the integral of the function

$400\int\left(1+\frac{2t}{24+t^2}\right)dt$

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$400\int\left(1+\frac{2t}{24+t^2}\right)dt$

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Learn how to solve problems step by step online. Find the integral int(400(1+(2t)/(24+t^2)))dt. The integral of a function times a constant (400) is equal to the constant times the integral of the function. Simplify the expression inside the integral. Rewrite the fraction \frac{t}{24+t^2} inside the integral as the product of two functions: t\frac{1}{24+t^2}. We can solve the integral \int t\frac{1}{24+t^2}dt by applying integration by parts method to calculate the integral of the product of two functions, using the following formula.

Final answer to the problem

$400t+400\ln\left(t^2+24\right)+C_0$

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 400(1+2t/(24+t^2))dt using partial fractionsSolve integral of 400(1+2t/(24+t^2))dt using basic integralsSolve integral of 400(1+2t/(24+t^2))dt using u-substitutionSolve integral of 400(1+2t/(24+t^2))dt using trigonometric substitution

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Function Plot

Plotting: $400t+400\ln\left(t^2+24\right)+C_0$

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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
D□x
∫
∫◻
|◻|
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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