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Find the integral of $\left(x+1\right)\left(x-4\right)$

Step-by-step Solution

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Final answer to the problem

$\frac{x^{3}}{3}-\frac{3}{2}x^2-4x+C_0$
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Step-by-step Solution

How should I solve this problem?

  • Find the integral
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Prove from LHS (left-hand side)
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1

Find the integral

$\int\left(x+1\right)\left(x-4\right)dx$
2

Rewrite the integrand $\left(x+1\right)\left(x-4\right)$ in expanded form

$\int\left(x^2-3x-4\right)dx$
3

Expand the integral $\int\left(x^2-3x-4\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately

$\int x^2dx+\int-3xdx+\int-4dx$
4

The integral $\int x^2dx$ results in: $\frac{x^{3}}{3}$

$\frac{x^{3}}{3}$
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5

The integral $\int-3xdx$ results in: $-\frac{3}{2}x^2$

$-\frac{3}{2}x^2$
6

The integral $\int-4dx$ results in: $-4x$

$-4x$
7

Gather the results of all integrals

$\frac{x^{3}}{3}-\frac{3}{2}x^2-4x$
8

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\frac{x^{3}}{3}-\frac{3}{2}x^2-4x+C_0$

Final answer to the problem

$\frac{x^{3}}{3}-\frac{3}{2}x^2-4x+C_0$

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Function Plot

Plotting: $\frac{x^{3}}{3}-\frac{3}{2}x^2-4x+C_0$

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1
2
3
4
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

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