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$\int\frac{x^5}{\sqrt{1+x^2}}dx$

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Solution

Final answer to the problem

$\frac{\sqrt{\left(1+x^2\right)^{5}}}{5}-\frac{2}{3}\sqrt{\left(1+x^2\right)^{3}}+\sqrt{1+x^2}+C_0$
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Step-by-step Solution

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We can solve the integral $\int\frac{x^5}{\sqrt{1+x^2}}dx$ by applying integration method of trigonometric substitution using the substitution

$x=\tan\left(\theta \right)$

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$x=\tan\left(\theta \right)$

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Learn how to solve problems step by step online. int((x^5)/((1+x^2)^(1/2)))dx. We can solve the integral \int\frac{x^5}{\sqrt{1+x^2}}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. Applying the trigonometric identity: 1+\tan\left(\theta \right)^2 = \sec\left(\theta \right)^2.

Final answer to the problem

$\frac{\sqrt{\left(1+x^2\right)^{5}}}{5}-\frac{2}{3}\sqrt{\left(1+x^2\right)^{3}}+\sqrt{1+x^2}+C_0$

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Function Plot

Plotting: $\frac{\sqrt{\left(1+x^2\right)^{5}}}{5}-\frac{2}{3}\sqrt{\left(1+x^2\right)^{3}}+\sqrt{1+x^2}+C_0$

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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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