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\int1\frac{}{}\cdot 4\cdot x\sqrt{9x^2+25}dx

Integrate x(9x^2+25)^0.5*4*/*1

Answer

$\int\sqrt{\frac{25}{9}+\frac{25}{9}\left(\sec\left(\theta\right)^2-1\right)}\tan\left(\theta\right)\left(\sec\left(\theta\right)^2-1\right)d\theta$

Step-by-step explanation

Problem

$\int1\frac{}{}\cdot 4\cdot x\sqrt{9x^2+25}dx$
1

Multiply $1$ times $4$

$\int\frac{}{}\cdot 4\sqrt{25+9x^2}xdx$

Unlock this step-by-step solution!

Answer

$\int\sqrt{\frac{25}{9}+\frac{25}{9}\left(\sec\left(\theta\right)^2-1\right)}\tan\left(\theta\right)\left(\sec\left(\theta\right)^2-1\right)d\theta$
$\int1\frac{}{}\cdot 4\cdot x\sqrt{9x^2+25}dx$

Main topic:

Integration by trigonometric substitution

Used formulas:

4. See formulas

Time to solve it:

1.83 seconds