Get the answer to "Evaluate the indefinite integral: ∫sec2xtan4xdx"

vomiderawo

Answered question

2021-11-22

Evaluate the indefinite integral:

\int \sec^{2} x \tan^{4} x d x

Symbee

Beginner2021-11-23Added 17 answers

Step 1
Evaluate the indefinite integral.

\int \sec^{2} x \tan^{4} x d x

Let

\tan (x) = t

\sec^{2} (x) d x = d t

Step 2

\int \sec^{2} (x) \tan^{4} (x) d x = \int t^{4} d t

= \frac{t^{5}}{5} + c

= \frac{\tan^{5} (x)}{5} + c

Mary Ramirez

Beginner2021-11-24Added 19 answers

Step 1: Use Integration by Substitution.
Let

u = \tan x, d u = \sec^{2} x d x

Step 2: Using u and du above, rewrite

\int \sec^{2} x \tan^{4} x d x

\int u^{4} d u

Step 3: Use Power Rule:

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C

\frac{u^{5}}{5}

Step 4: Substitute

u = \tan x

back into the original integral.

\frac{\tan^{5} x}{5}

Step 5: Add constant.

\frac{\tan^{5} x}{5} + C

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