Question: "Find the indefinite integral. ∫x2sec⁡h2x3dx"

nicekikah

Answered question

2021-11-08

Find the indefinite integral.

\int x^{2} {\sec h}^{2} x^{3} d x

Nathanael Webber

Skilled2021-11-09Added 117 answers

Step 1
Our Aim is to find the indefinite integral given below:−

\int x^{2} {\sec h}^{2} (x^{3})

...(i)
Step 2
Consider the integral given by equation−(i), we have:−

\int x^{2} {\sec h}^{2} (x^{3}) d x

...(i)
Let

x^{3} = u

\Rightarrow 3 x^{2} \frac{d x}{d u} =

\Rightarrow x^{2} d x = \frac{d u}{3}

Putting the value of

x^{2} d x

in equation−(i), we have:−

\Rightarrow \int x^{2} {\sec h}^{2} (x^{3}) d x = \frac{1}{3} \int {\sec h}^{2} (u) d u

\Rightarrow \int x^{2} {\sec h}^{2} (x^{3}) d x = \frac{1}{3} \tan h (u) + c

Answer:

\Rightarrow \int x^{2} {\sec h}^{2} (x^{3}) d x = \frac{1}{3} \tan h (x^{3}) + c

(Putting

u = x^{3}

)

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