1. calculators
  2. Basic Integrals

Basic Integrals Calculator

Get detailed solutions to your math problems with our Basic Integrals step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

Go!
Go!
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

1

Solved example of basic integrals

$\int\frac{x^2}{\sqrt{x}}$
2

Simplify the fraction $\frac{x^2}{\sqrt{x}}$ by $x$

$\int\sqrt{x^{3}}dx$

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $\frac{3}{2}$

$x^{\left(\frac{3}{2}+1\right)}\frac{1}{\frac{3}{2}+1}$

Add the values $\frac{3}{2}$ and $1$

$\frac{2}{5}\sqrt{x^{5}}$
3

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $\frac{3}{2}$

$\frac{2}{5}\sqrt{x^{5}}$
4

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

$\frac{2}{5}\sqrt{x^{5}}+C_0$

Final Answer

$\frac{2}{5}\sqrt{x^{5}}+C_0$

Struggling with math?

Access detailed step by step solutions to thousands of problems, growing every day!