What is the integral of (3+7x^2)^95x ?

The integral of (3+7x^2)^95x is 1/28 (3+7x^2)^{10}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3+7x^2)^95x

\int (3 + 7 x^{2})^{9} 5 x d x

\frac{1}{28} (3 + 7 x^{2})^{10} + C

Solution steps

\int (3 + 7 x^{2})^{9} \cdot 5 x d x

Take the constant out:

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

= 5 \cdot \int (3 + 7 x^{2})^{9} x d x

Apply u-substitution

: \int \frac{u ^{9}}{14} d u

= 5 \cdot \int \frac{u ^{9}}{14} d u

Take the constant out:

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

= 5 \cdot \frac{1}{14} \cdot \int u^{9} d u

Apply the Power Rule

: \frac{u ^{10}}{10}

= 5 \cdot \frac{1}{14} \cdot \frac{u ^{10}}{10}

Substitute back

u = 3 + 7 x^{2}

= 5 \cdot \frac{1}{14} \cdot \frac{( 3 + 7 x ^{2} ) ^{10}}{10}

Simplify

5 \cdot \frac{1}{14} \cdot \frac{( 3 + 7 x ^{2} ) ^{10}}{10} : \frac{1}{28} (3 + 7 x^{2})^{10}

= \frac{1}{28} (3 + 7 x^{2})^{10}

Add a constant to the solution

= \frac{1}{28} (3 + 7 x^{2})^{10} + C

\int (7 x^{2} + 1) d x

\int \frac{2}{x ^{5}} + \frac{1}{x} d x

\int \frac{cos ( 6 x )}{cos ^{2} ( 3 x )} d x

\int \frac{8}{x ( 1 + 8 x ) ^{5}} d x

What is the integral of (3+7x^2)^95x ?
The integral of (3+7x^2)^95x is 1/28 (3+7x^2)^{10}+C