Find the integral of -x2-a2 with respect to x and evaluate -16 x2-25 d x-

∫√(x^2+a^2) = x/2√(x^2 + a^2) + a^2/2log(x+√(x^2+a^2)) + c for the derivation I = ∫√(16x^2 + 25) dx = ∫√((4x)^2 + (5)^2) dx = [ 4x/2√(16x^2 + 25) + 25/2log | 4x ...

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Byju's Answer

Standard XII

Mathematics

Integration by Parts

Find the inte...

Question

Find the integral of $\sqrt{x^{2} + a^{2}}$ with respect to $x$ and evaluate $\int \sqrt{16 x^{2} + 25} d x$ .

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Solution

$\int \sqrt{x^{2} + a^{2}} = \frac{x}{2} \sqrt{x^{2} + a^{2}} + \frac{a^{2}}{2} log (x + \sqrt{x^{2} + a^{2}})$ + c for the derivation

I = $\int \sqrt{16 x^{2} + 25}$ dx

= $\int \sqrt{(4 x)^{2} + (5)^{2}}$ dx

= $[\frac{4 x}{2} \sqrt{16 x^{2} + 25} + \frac{25}{2} log ∣ ∣ 4 x + \sqrt{16 x^{2} + 25} ∣ ∣] + c$

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Find the integral of √x2+a2 with respect to x and evaluate ∫√16x2+25 dx.

∫√x2+a2=x2√x2+a2+a22log(x+√x2+a2) + c for the derivation I = ∫√16x2+25 dx = ∫√(4x)2+(5)2 dx = [4x2√16x2+25+252log∣∣4x+√16x2+25∣∣]+c

Find the integral of $\sqrt{x^{2} + a^{2}}$ with respect to $x$ and evaluate $\int \sqrt{16 x^{2} + 25} d x$ .