CLASE MARTES 20 ABRIL
∫𝑆𝑒𝑛5𝑥 𝑑𝑥
𝐶𝑜𝑠45𝑥 =- 1
5∫𝑑𝑡
𝑡4 = - 1
5 ∫𝑡−4𝑑𝑡 = - 1
5 𝑡−3
−3 + c = 1
15𝑡3 + c = 1
15𝐶𝑜𝑠35𝑥 + c
𝑡 = cos 5x, dt =-5Sen 5x dx ,- 𝑑𝑡
5 = Sen5x dx
6.∫𝑥𝑑𝑥
√𝑥2+1 = 1
2 ∫𝑑𝑡
√𝑡 = 1
2 ∫𝑡−1
2𝑑𝑡 = 1
2 𝑡1
2
1
2
+ c = 𝑡1
2 + c = √𝑥2+ 1 + c
𝑡 = x2 + 1, dt = 2xdx. 𝑑𝑡
2 =x dx
7.∫𝑥𝑑𝑥
√𝑥4+1 = 1
2∫𝑑𝑡
√𝑡2+1 = 1
2 Ln|𝑡 + √𝑡2+ 1|+ c = 1
2𝐿𝑛|𝑥2+ √𝑥4+ 1|+ c
𝑡 = x2, dt = 2xdx
𝑡 = x4 = (𝑥2)2
∫𝑥2+2𝑥
√𝑥3+3𝑥2+5dx = 1
3∫𝑑𝑡
√𝑡 = 1
3𝑡1
2
1
2
+ c = 2
3√𝑡 + c = 2
3√𝑥3+ 3𝑥2+ 5 + c
𝑡= x3 + 3x2 + 5, dt = (3x2 + 6x)dx = 3(x2 + 2x)dx
∫𝑥3𝑑𝑥
(1−2𝑥4)5 = - 1
8 ∫𝑡−5 𝑑𝑡 = - 1
8 𝑡−4
−4 + c = 1
32𝑡4 + c = 1
32(1−2𝑥4)4 + c
𝑡 = 1 – 2x4, dt = -8x3dx, 𝑑𝑡
− 8 = x3dx
𝑡 = (1- 2x4)5, dt = 5(1 – 2x4)4(-8x3)dx
9.∫𝑥3𝑑𝑥
√1−2𝑥2 = - 1
4∫1−𝑡
2𝑑𝑡
√𝑡 = - 1
8∫(1−𝑡)𝑑𝑡
𝑡1
2 = - 1
8∫(𝑡−1
2− 𝑡1
2)𝑑𝑡 = - 1
8 (𝑡
1
2
1
2−𝑡3
2
3
2
)+ c =
= - 1
4√1 − 2𝑥2 + 1
12 (√1 − 2𝑥2)3 + c
𝑡 = 1 – 2x2, dt = - 4xdx , 𝑑𝑡
− 4 = xdx, x3 dx= x2. Xdx
2x2 = 1 – t, x2 = 1−𝑡
2 1−𝑡
𝑡1
2 = 1
𝑡1
2−𝑡
𝑡1
2 = 𝑡−1
2 - 𝑡1
2
𝑎−𝑏
2 =𝑎
2−𝑏
2
