What is the integral of (x^2y-ln(cos(x))) ?

The integral of (x^2y-ln(cos(x))) is -ln(cos(x))y+(x^2y^2)/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2y-ln(cos(x)))

\int (x^{2} y - ln (cos (x))) d y

- ln (cos (x)) y + \frac{x ^{2} y ^{2}}{2} + C

Solution steps

\int x^{2} y - ln (cos (x)) d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int ln (cos (x)) d y + \int x^{2} y d y

\int ln (cos (x)) d y = ln (cos (x)) y

\int x^{2} y d y = \frac{x ^{2} y ^{2}}{2}

= - ln (cos (x)) y + \frac{x ^{2} y ^{2}}{2}

Add a constant to the solution

= - ln (cos (x)) y + \frac{x ^{2} y ^{2}}{2} + C

\int \frac{1}{x 2 x - 1} d x

y = x (x - 10)

y = x^{4} + 2 e^{x} (0.2)

\int_{0}^{1} 1 - x^{2} d x

\frac{d}{d x} (cot^{2} (7 x))

What is the integral of (x^2y-ln(cos(x))) ?
The integral of (x^2y-ln(cos(x))) is -ln(cos(x))y+(x^2y^2)/2+C