Find the indefinite integral.

Linda Seales
2021-12-11
Answered

Find the indefinite integral.

You can still ask an expert for help

Jenny Sheppard

Answered 2021-12-12
Author has **35** answers

Step 1

We have to solve the indefinite integral:

Solving the integral by substitution method.

Assuming,

Differentiating,

Step 2

Substituting above values in the given integral, we get

Hence, value of given indefinite integration is

Elois Puryear

Answered 2021-12-13
Author has **30** answers

Given:

$\int {\mathrm{sec}}^{2}\left(x\right)\sqrt{3}\left\{\mathrm{tan}\left(x\right)\right\}dx$

Substitution$u=\mathrm{tan}\left(x\right)\Rightarrow \frac{du}{dx}={\mathrm{sec}}^{2}\left(x\right)$

$=\int \sqrt{3}\left\{u\right\}du$

Integral of a power function:

$\int {u}^{n}du=\frac{{u}^{n+1}}{n+1}$ at $n=\frac{1}{3}:$

$=\frac{3{u}^{\frac{4}{3}}}{4}$

Reverse replacement$u=\mathrm{tan}\left(x\right):$

$=\frac{3{\mathrm{tan}}^{\frac{4}{3}}\left(x\right)}{4}$

$\int {\mathrm{sec}}^{2}\left(x\right)\sqrt{3}\left\{\mathrm{tan}\left(x\right)\right\}dx$

$=\frac{3{\mathrm{tan}}^{\frac{4}{3}}\left(x\right)}{4}+C$

Substitution

Integral of a power function:

Reverse replacement

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