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Find the integral $\int\left(x+x^2\right)fxdx$

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Solution

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Final Answer

$\frac{x^{3}f}{3}+\frac{x^{4}f}{4}+C_0$
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Step-by-step Solution

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1

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

$f\int\left(x+x^2\right)xdx$
2

Rewrite the integrand $\left(x+x^2\right)x$ in expanded form

$f\int\left(x^2+x^{3}\right)dx$

Learn how to solve trigonometric identities problems step by step online.

$f\int\left(x+x^2\right)xdx$

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Learn how to solve trigonometric identities problems step by step online. Find the integral int((x+x^2)fx)dx. The integral of a function times a constant (f) is equal to the constant times the integral of the function. Rewrite the integrand \left(x+x^2\right)x in expanded form. Expand the integral \int\left(x^2+x^{3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Solve the product f\left(\int x^2dx+\int x^{3}dx\right).

Final Answer

$\frac{x^{3}f}{3}+\frac{x^{4}f}{4}+C_0$

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 (x+x^2)fdx using basic integralsSolve integral of (x+x^2)fdx using u-substitutionSolve integral of (x+x^2)fdx using integration by partsSolve integral of (x+x^2)fdx using trigonometric substitution

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Function Plot

Plotting: $\frac{x^{3}f}{3}+\frac{x^{4}f}{4}+C_0$

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5
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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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$\frac{1-\sin\left(x\right)}{\cos\left(x\right)}=\frac{\cos\left(x\right)}{1+\sin\left(x\right)}$

Main Topic: Trigonometric Identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined.

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