What is the integral of 7xsqrt(1-x^4) ?

The integral of 7xsqrt(1-x^4) is 7/4 (arcsin(x^2)+1/2 sin(2arcsin(x^2)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7xsqrt(1-x^4)

\int 7 x 1 - x^{4} d x

\frac{7}{4} (arcsin (x^{2}) + \frac{1}{2} sin (2 arcsin (x^{2}))) + C

Solution steps

\int 7 x 1 - x^{4} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int x 1 - x^{4} d x

Simplify

x^{4} : (x^{2})^{2}

= 7 \cdot \int x 1 - (x^{2})^{2} d x

Apply u-substitution

: \int \frac{1 - u ^{2}}{2} d u

= 7 \cdot \int \frac{1 - u ^{2}}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \frac{1}{2} \cdot \int 1 - u^{2} d u

Apply Trigonometric Substitution

: \int cos^{2} (v) d v

= 7 \cdot \frac{1}{2} \cdot \int cos^{2} (v) d v

Rewrite using trig identities

= 7 \cdot \frac{1}{2} \cdot \int \frac{1 + cos ( 2 v )}{2} d v

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \int 1 + cos (2 v) d v

Apply the Sum Rule:

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

= 7 \cdot \frac{1}{2} \cdot \frac{1}{2} (\int 1 d v + \int cos (2 v) d v)

\int 1 d v = v

\int cos (2 v) d v = \frac{1}{2} sin (2 v)

= 7 \cdot \frac{1}{2} \cdot \frac{1}{2} (v + \frac{1}{2} sin (2 v))

Substitute back

= 7 \cdot \frac{1}{2} \cdot \frac{1}{2} (arcsin (x^{2}) + \frac{1}{2} sin (2 arcsin (x^{2})))

Simplify

7 \cdot \frac{1}{2} \cdot \frac{1}{2} (arcsin (x^{2}) + \frac{1}{2} sin (2 arcsin (x^{2}))) : \frac{7}{4} (arcsin (x^{2}) + \frac{1}{2} sin (2 arcsin (x^{2})))

= \frac{7}{4} (arcsin (x^{2}) + \frac{1}{2} sin (2 arcsin (x^{2})))

Add a constant to the solution

= \frac{7}{4} (arcsin (x^{2}) + \frac{1}{2} sin (2 arcsin (x^{2}))) + C

\frac{d}{d x} (\frac{1}{2 x - 5})

f (2) = 4 lo g_{6} (x)

\frac{d}{d x} (2^{x} + 3)

x y^{^{'}} + y (1 + ln (x y)) = 0

\int 8 x d x

What is the integral of 7xsqrt(1-x^4) ?
The integral of 7xsqrt(1-x^4) is 7/4 (arcsin(x^2)+1/2 sin(2arcsin(x^2)))+C