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Chapter 5: Q 44. (page 429)

Solve the integral:鈭�3x+1secxdx

Short Answer

Expert verified

The required answer is3x+1sinx+3cosx+c.

Step by step solution

01

Step 1. Given information. 

We have given integral is鈭�3x+1secxdx.

02

Step 2. Solve the integration by parts .  

We have,

u=3x+1du=3dx

and

dv=cosxdxv=鈭�cosxdxv=sinx

The formula of integration by parts is 鈭�udv=uv-鈭�vdu.

localid="1648742547412" 鈭�3x+1secxdx=(3x+1)sinx-鈭�3sinxdx=(3x+1)sinx-3鈭�sinxdx=(3x+1)sinx-3(-cosx)+c=(3x+1)sinx+3cosx+c

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