Find out the answer to "Evaluate the indefinite integral. ∫(x2−sec2x)dx"

Michelle Isakson

Answered question

2021-11-19

Evaluate the indefinite integral.

\int (x^{2} - \sec^{2} x) d x

Maked1954

Beginner2021-11-20Added 17 answers

Step 1
To integrate:

\int (x^{2} - \sec^{2} x) d x

Evaluating the integral.

\int (x^{2} - \sec^{2} x) d x = \int x^{2} d x - \int \sec^{2} x d x

= \frac{x^{3}}{3} - \tan x + C

Step 2
Hence, required answer is

\frac{x^{3}}{3} - \tan x + C

Egreane61

Beginner2021-11-21Added 16 answers

Step 1: Expand.

\int x^{2} - \sec^{2} x d x

Step 2: Use Sum Rule:

\int f (x) + g (x) d x = \int f (x) d x + \int g (x) d x

\int x^{2} d x - \int \sec^{2} x d x

Step 3: Use Power Rule:

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

\frac{x^{3}}{3} - \int \sec^{2} x d x

Step 4: The derivative of

\tan x i s \sec^{2} x

\frac{x^{3}}{3} - \tan x

Step 5: Add constant.

\frac{x^{3}}{3} - \tan x + C

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