# Step-by-step Solution

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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Step-by-step explanation

Problem to solve:

$\int\sec\left(5x\right)\cdot\tan\left(5x\right)dx$

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

$u=5x$

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sec(5*x)*tan(5*x))dx. We can solve the integral \int\sec\left(5x\right)\tan\left(5x\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 5x it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation. Substituting u and dx in the integral and simplify.

$\frac{1}{5}\sec\left(5x\right)+C_0$
$\int\sec\left(5x\right)\cdot\tan\left(5x\right)dx$

### Main topic:

Trigonometric integrals

### Time to solve it:

~ 0.08 s (SnapXam)