Question

Evaluate ∫ 3ax/(b2 +c2x2) dx​

Answer 1

Step-by-step explanation:

HOPE THE ATTACHMENT HELPS YOU

Answer 2

At last we get the value of ∫ 3ax/($b^2 +c^2x^2$) dx  which is  $(3a/c) ln|b^2 + c^2x^2| + C$.

Integration is a technique for combining or merging the parts to get at the total.

Sign of integration is ∫dx.

The main applications of integration are computing the volumes of three-dimensional objects and determining the areas of two-dimensional regions.

To evaluate the given integral,

$u = b^2 + c^2x^2$

du/dx = 2cx

By taking integration we get

∫ 3ax/($b^2 +c^2x^2$) dx = (3a/c) ∫ du/u

Integration of ∫ du/u is $ln|u| + C$

∫ 3ax/($b^2 +c^2x^2$) dx = $(3a/c) ln|u| + C$

By substituting value of given value of u,

∫ 3ax/($b^2 +c^2x^2$) dx= $(3a/c) ln|b^2 + c^2x^2| + C$

By substituting back in terms of x, we get

∫ 3ax/($b^2 +c^2x^2$) dx = $(3a/c) ln|b^2 + c^2x^2| + C$

Hence, The provided integral's answer is this.

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