Evaluate <mrow> 7 x 3 </mrow>

Amappyaccon22j7e

Amappyaccon22j7e

Answered question

2022-05-11

Evaluate 7 x 3 4 ( ( 5 x 4 + 4 ) 2 + 1 )  d x.

Answer & Explanation

Lucille Lucas

Lucille Lucas

Beginner2022-05-12Added 16 answers

Since 74 is constant with respect to x, move 74 out of the integral.

74x3(5x4+4)2+1dx

Let u=5x4+4. Then du=20x3dx, so 120du=x3dx. Rewrite using u and du.

741u2+1120du

Simplify.

74120(u2+1)du

Since 120 is constant with respect to u, move 120 out of the integral.

74(1201u2+1du)

Simplify the expression.

780112+u2du

The integral of 112+u2 with respect to u is arctan(u)+C.

780(arctan(u)+C)

Simplify.

780arctan(u)+C

Replace all occurrences of u with 5x4+4.

780arctan(5x4+4)+C

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