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\int x\sec\left(9x\right)^2\cdot dx

Integrate sec(9x)^2*x

Answer

$\frac{1}{81}\ln\left|\cos\left(9x\right)\right|+\frac{1}{9}x\tan\left(9x\right)+C_0$

Step-by-step explanation

Problem

$\int x\sec\left(9x\right)^2\cdot dx$
1

Use the integration by parts theorem to calculate the integral $\int\sec\left(9x\right)^2xdx$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Unlock this step-by-step solution!

Answer

$\frac{1}{81}\ln\left|\cos\left(9x\right)\right|+\frac{1}{9}x\tan\left(9x\right)+C_0$
$\int x\sec\left(9x\right)^2\cdot dx$

Main topic:

Integration by parts

Used formulas:

2. See formulas

Time to solve it:

~ 1.85 seconds